Lili and Molly fighting

I've not been on in a long time but I'm back because of problems
We rehomed from a rescue an eleven week old pup about half a year ago. That's Molly. Up until very recently they have been fine together. Molly bothered Lili (our one year old pug) a lot by trying to play fight with her all the time, but nothing ever happened and recently Molly has improved massively. They've never had a fight until... Two days ago? Very recently anyway.
Firstly I'd like to say both girls were spayed about two weeks ago. Lili had problems and had to take extra painkillers, obviously she took longer to recover but seemed normal after a week.
I think the first fight was over food. Lili had finished her breakfast first and went over to Molly who was still eating. Molly growled but Lili kept snuffling about, a fight followed. Afterwards they were seperated.
They were fine again later, the were walked together and so on, until that night when Molly was sleeping on the couch, Lili jumped on her by accident. Molly snapped at Lili and Lili got really angry, they had a big fight and had to be seperated. Lili took ages to calm down.
Yesterday they were just playing, chasing each other round the living room table and jumping about. Lili jumped on Molly from the couch. Molly got a bit of a fright but did nothing, not even a yelp. Then they walked about for a bit and Lili just attacked Molly, I don't think Molly was even doing anything. It was very strange as the previous night they had both slept in my daughter's bed happily together without a fuss, and were walked together without a problem earlier. They were seperated again, but I had to go to Dundee and I took Lili. When I got back the dogs were reintroduced and seemed okay, they were walked together by my two daughters and nothing happened, Lili was off lead. Molly was on the flexi lead.
After the walk we kept them both out but they were on their leads. Lili wandered about in the kitchen (dinner was being made) by herself and Molly was just sitting sucking on her cushion that she loves. We did this for about half an hour them Molly was put in the kitchen (where she sleeps.)
This morning my daughter got up to take them out. She fed them separately and put on their harnesses and let them meet on lead. They sniffed each other and Molly playfully snapped at Lili a few times but never caught her, there was no reaction from Lili either. Then she got up to take them out and once again Lili just attacked Molly for no reason. Molly's hackles didn't even go up and after a few seconds she stopped fighting. My daughter had them on their leads holding them apart and Lili was so angry, she just wouldn't stop trying to get Molly. Molly didn't do a thing. They were once again separated and walked seperately too. They've been seperated since.
This is very distressing for us and the thought of rehoming Molly is so sad, especially as she has done nothing wrong. We're hoping to see a behaviorist as rehoming is such a sad option. I've heard once bitches start to fight they end up fighting forever, but I hope there is a chance here . Molly is doing nothing wrong! She never starts the fights.
One last thing, the vet said Lili was slightly chubby and she was to get reduced food and it was to be special neutered food. This made her very grumpy so we stopped reducing her food. I know we shouldn't but she was so unhappy. Ever since the fighting has started Lili has also been grumpy with everything, barking at cars, dogs, people, etc. She was always such a cheery wee dog.
Any advice?

Maybe visiting the vet first to see if their is any other underlining issues just to tick boxes then if everything if fine health wise then a behaviourist should be able to help..thats my opinion anyway

Spayed two weeks ago, they may well be healed on the outside but will still be healing on the inside, so rough play should still be curbed. As for playful snapping, I'm with Lilli I'd get pretty stroppy too if someone kept snapping at me and wouldn't take a hint. Molly has no manners and it's not Lillii's job to teach her how to behave it's yours. step in sooner and tell her to "pack it in" the second she starts.I don't understand why you think she does nothing wrong and never starts the fights when it sounds to me like she is provoking Lilli.
As for reduced rations Lilli will be seeking out food because she hungry just stay in the room while they eat and don't allow them to encroach on the other. Reducing her normal food will work you don't need "diet food" Why not give Lilli a bone to keep her busy? my Pugs would gnaw away at a bone all day given half a chance.

Trouble, I can see your concern with Molly and it is something that is bothering me too, but I don't just stand around and let her snap. I always tell her to stop as soon as she snaps and as I said she has improved a lot recently, it was just this morning when she did it again and was immediately prevented. And 'snap' isn't really the correct word for what she did this morning, it was more mouthing, if you know what I mean?
Also, as for the food it wasn't our decision, the vet suggested it.
Just to clarify, by saying Molly is doing nothing wrong, I mean when they actually fight - she often stops defending herself and shows no aggression when she sees Lili, even looking happy to see her. If Molly actually fought I'm sure Lili would have got injured, but she hasn't even got scratched, thank god. Thank you for your advice though, and we'll definitely get Lili a bone to chew on - do you think we should put them on leads again in the house?
We'll be going to the vet soon. Last time he said one of them had a rooting tooth, if that could be a factor, I don't know.
Thank you, both of you

I'm sorry you are having problems with your two girls. I would definitely get both dogs checked out at the vets. 2 weeks post-operative is not long and the fact that you say their behaviour has changed in the last few days could be well be due to pain with one or both of them.

You have got to be aware of their flash-points and step in before they kick-off. If problems tend to occur during food time, feed them separately, or you stand between them so that they both get a chance to eat their food without the other bothering them. My two (littermate brothers) can be a pain during food time and I always stand between them so no nonsense starts.

A good behaviourist could well be able to sort them out but until you get one in, try and just be aware of any behaviour that looks as though something is about to start up and immediately stop it by diverting their attention i.e. putting them into a sit and give them a treat.

A friend of mine has two bitches who use to fight and one of them ended up with half an ear missing. She got a good behaviourist in (from Kent so alas no good for you) and he showed her exactly what to do and they now live quite happily together.

Good luck and keep us informed as to how you get on.