Thank you all so much for your advice. I'll have a look at the BAT training videos, although once she's spotted something it's hard to distract her with food, even though she loves it.
I've had a couple of emails from the behaviourist asking how I'm getting on, but as it's not improved I just said what I was doing and thanks very much!
I felt much better with her wearing a muzzle, but it made her much worse and she would lunge and spin trying to remove it (actually foaming at the mouth).
My husband isn't keen to keep going to more training classes (we've been to 3 lots plus the behaviourist) and just says accept her for how she is, but I dream of that time when I could walk as a normal dog walker! He just says well I should have got a puppy then and not a rescue dog - true but not helpful ha, ha. She is a dream dog at home, poor thing. The closest she comes to normal behaviour is there is a dog next door who has made a hole in the fence and they sometimes see each other, wag tails and smell each other - that makes me thing there is hope!

It's all about timing!
If you read up on BAT you will learn to notice the signs that say, "I'm about to go into orbit"' and act BEFORE she gets that far.

I should maybe say here that she should be on a training lead all the time when in public. A long, light nylon flat lead (not cord) is better than a retractable one - you can let it hang loose, paying it out/gathering it in as necessary, or even letting it drag on the ground so she barely realises she's ON a lead.

To begin with, just her noticing the other dog is all you look for. Her head will come up, eyes fastened on the dog. She might stop in her tracks. Her mouth will probably close.

The MOMENT she does, call her and say, "This Way!", about turn, and walk away in the opposite direction. If you need to, give a GENTLE tug on the lead. Throw a treat on the ground in the direction you are going, encouraging her to come running to you. High value 'soft and smelly' treats work well, and ones that show up against the ground - cubes of cheese or frankfurter sausage are good.

If you are in a field or park and see a dog, walk around it in a wide semi-circle, doing everything you can to keep your dog's attention on you. Praise, chatter, treat continuously (the tube of liver paste is great for this), offer a toy, anything, it doesn't matter!

If she sees the dog and halts, you're too close, move further away until she relaxes more.

It's a system of avoidance, of setting your dog up for success, patience, time, and consistency.

Another thing you can do is to find a park bench out of the way, and practise 'down-stay'. Use frequent treats when she sees another dog - literally praise her for noticing it! 'Doggie? Yes! good girl!' Etc. if a dog starts heading in your direction, get up and move away from it, calling her to you and keeping your voice up-beat and playful. Don't force her to encounter it - she will become more relaxed about dogs as she learns to trust you.

It's taken her all this time in her life to learn to defend herself as she currently does. It's not going to take five minutes to unlearn it!

Remember too, that just like us, dogs have build-ups of stress that eventually leads to them exploding at what you may think is a completely benign situation. Every dog your girl sees is another stressful situation, whether or not she's got past it without attacking. One she might be fine with, 2 might be pushing it, 3 and her stress-levels will be high - the 4th might be the one that tips her over the edge! So give her time out frequently, allow her space and the time to totally relax after each encounter. That might mean you have to go home/back to the car just five minutes after you set out, but that's OK - better a short, successful outing than a longer, disastrous one.

You don't need to 'accept her as she is' - she's not happy with how she is, why should you be? I do agree about not throwing good money after bad, however.

As for having a pup instead - heck, they come with their own set of problems! ANY dog you had was going to be a problem in one way or another. You sound as if you've been very lucky with this one, it's just other dogs she has the issue with, and you can do something about that.

Chin up, don't feel despondent! You're doing all the right things, and If you follow BAT too, you'll get there and you'll have the dog you want. You have only just begun your journey together! If you have a setback, don't worry too much: try to work out why it happened, and then you can try to avoid that happening again.

Best of luck and keep us posted!

Just a quick post . Did you conditioner her to wearing a muzzle at home first ? Most dogs hate muzzles especially if they are not used to wearing one and it adds to their stress but they can become used to it if you carefully introduce it.
I dont think its worth you going to any more training classes at the moment , it will just stress her out she's not likely to learn anything.

What exactly did your behaviourist say to do when faced with other dogs . i think you should be honest with her , and say your dog hasnt inproved . its not your fault and things often need to be adjusted . I'm really sure she wants to know if its not working , any genuine behaviourist would. All feedback from their customers is important and also you paid alot of money and you deserve your moneys worth .

Never give up hope with Delilah. You did a very kind thing in giving her a home .
if you hadnt , where would she be now , still in a rescue or a yo yo dog . Tell your husband that even puppies can end up fear aggressive if they are attacked.

Most dogs end up barking at each other through the fence so I'm impressed that the two dogs appear to be friendly towards each other, would it be possible for Delilah to meet the neighbours dog properly ? it would bea good chance for her to socialise and relax with another dog .

Pon lady , thats lots of useful advice . havent had time to look at link yet but it is something to look forward too.
Grisha is very much admired in the dog world.
I meant to buy her book about Control unleashed about LAT .
I assume she has moved on from Look at that , rewarding for looking at the scary thing?

ETA there is also CAT “Constructional Aggression Treatment but it doesnt sound practical to me , you dont remove your dog but remove the trigger eg the other dog !
CAT, BAT, LAT Trainer love their acronyms!

Yes, I think if you have a dog that does actually bite and not just bark then it would be a very good idea to use one , the safety of other dogs is important .

Well, I never say that Jade "does" bite. She's never bitten anybody or any dogs. BUT, at the same time, I've seen her lunge for a child's face with true intent to do harm, and while muzzled, she viciously "attacked" a small dog that ran up to her with aggression. She could not bite, but boy was she trying.

I'm more concerned with potential euthanasia were she to badly bite a child. If she were not a threat to kids, I likely wouldn't bother muzzling her. There are often strays and dangers here, and I hate her not being able to defend herself as it is. Her being a threat to dogs whose owners won't keep them restrained would not make me muzzle.

Perhaps that sounds rough, but my dogs really need to defend themselves and only the extreme threat she poses to humans makes me muzzle.

Thats a good point about muzzled dogs not being able to defend themselves against attacks.
So taking into account the area where you live and how the other dogs and their owners behave is important. if Jade is in danger I dont think you are being rough in not wanting to muzzle her but like you said if a dog bites a child or person badly then it would be destroyed.
You can also be sued even for even small bites due to this compensation culture.

I saw a massive dog this afternoon in the distance , i think it was a white dog de bordeaux but I'm not sure.
I had to admit that i veered off in another direction not just because of it's size but because of the way the owner was handling it . It was on a harness and lead and it was pulling its owner along and he kept yanking it back and smacking it . I wasnt close enough to shout ," lay off " like I usually do !

The dog was fine but with an owner like that , how will it end up and such a huge dog.

She is scared of adults, she's no threat to them. She's a 55 lb, 11 year old, rickety dog. But she can be nasty and she poses a true threat to children. Not only would it break my heart to see a child badly bitten, she stands a true chance of euthanasia, as well in that particular case. She's a GSD/Pit Bull mix, and old to boot, so they'd almost certainly put her down. They rarely/never euthanize for fights between dogs.

I carry a fire poker and have had to use it before. I also only walk her with big Nigredo. He's a massive dude and I've seen dogs think twice before walking up on us, and decide against it. We just do what we can, and hope for the best. I've had no severe issues with these two, so all good.

CAT can be successful providing the trainer knows exactly what they're doing. It's not something though I'd try myself. Georgina, my Shar-Pei despite all the problems we had when she was partially sighted has developed into very calm, confident dog. She's never been DA and even when surrounded by dogs "playing the fool" or displaying aggression she remains self composed. Gabor her trainer, who specialises in rehabilitating aggressive dogs sometimes uses her as a decoy for his less serious cases. The first time he used her was with a GSD who was barking and lunging at her. I watched with my heart in mouth as Gabor walked her past the dog and his owner. After about 10 minutes of variations (circling, figures of eight etc) the GSD stopped barking and lunging to the point where the owner and Gabor were able to walk the two dogs together and do the normal training routine. We often see the GSD at training and he'll walk past Georgina with no sign of aggression towards her. An added bonus is that my Miniature Schnauzer who when he first started training had some fear aggression towards larger dogs, has learnt from her to ignore other dogs.

I think LAT is a part of BAT, but rather than simply giving the dog a treat reward, it also gets the 'reward' of avoiding the situation which is worrying it. Double win means the results are often faster than LAT alone. That doesn't mean LAT isn't a useful thing to do, though, it is! I have a mobility problem so to practise soothing my dog when he sees others, without needing to March about, is a good thing.

I haven't come across the acronym CAT, I'm assuming you keep the dog in one place and use a trigger to walk past, perhaps getting closer each time? I don't think this is as constructive because the dog needs to learn when it encounters a trigger, it can deal with the situation by turning back to its owner, rather than 'keep very still and the trigger will go away' which of course doesn't happen in real life!

I am in the UK where BAT is very new and not many behaviourists know about it or are trained in it - I just struck lucky!

This is maybe not the thread to say this . . . I do think for £200, more than twice what I paid, that the OP deserves far more from her behaviourist than she's been given. Everyone has to start somewhere, it's true, and bonding with a rescue by using basic training or getting the dog used to a clicker, is always advisable, but most of us can surely figure that out for ourselves? Especially the OP, who says she's been to three lots of training classes! The behaviourist was hired to deal with a specific issue, and if it was simply too early in the dog's rehab to address that issue, the OP should have been told that, and invited back to a second free consultation later on to deal with the actual problem she'd been hired for!

I hate to say that this behaviourist has given poor value for money but it does seem that way, and the result is that the client is now reluctant to seek out another behaviourist that might have been able to help.

I hope the online free material Grisha provides helps the OP and her dog to address the dog aggression. Thank goodnes there are behaviourists who genuinely want to help, not just to make money!