Hi muttzrule ~ I do feel for you ~ it must be difficult trying to be the peace keeper in a bit of a war zone! Now you've given me so much more info, pehaps I can suggest things that may help. But I think it will mean going back to basics for a while.
Firstly, is Thurston neutered? If not, get him done pronto!
As a bit of background, cats are very territorial creatures & most aggression between cats (& dogs in some cases) is caused by a need for territory. This includes both a core territory, where they can sleep, rest, eat & take care of bodily functions like grooming ~ in most cases this is the owner's home. But cats also need a wider territory to provide an area big enough to find prey & feed themselves, to find a mate, rear kittens etc.
Despite cats now being the most common pet in the UK, there are still question marks over whether they are really a domesticated species in the true sense of the word. And humans have had nowhere near the input into selective breeding as they have in other species. This means that cats' behaviours are still effectively "wild", biologically hardwired & ingrained, so this is why they stilll have these territorial needs & why they will still hunt prey, despite having a nice home & all they want to eat.
Most intercat conflict is caused by a perceived lack of the key resources that cats need for survival. This means things like warmth, sleeping & resting places, litter trays, food, water, scratching posts, social interactions & territory. If these resources are abundantly supplied then the chances of conflict are reduced & personally I think the best way to modify unwanted cat behaviours is to increase these key resources.
So for Thurston & Kobie, I would firstly have a look at where they sleep & where they choose to sleep & increase the availability of beds & resting places in these areas. Beds in warm, draft-free places, preferably at different heights should be provided, in different rooms depending on where they like to rest/sleep.
If your cats like to graze on dry food throughout the day, maybe put several feeding stations around the house (maybe windowsills where Moxie can't pinch the cat food?) & several watering places. Food & water don't need to be close together ~ they rarely are in the wild!
Cats can learn to time share overlapping territories so maybe observe when Kobie is more active, where he goes, & try to keep Thurston away at these times. Thurston can have access when Kobie is sleeping. But most important for Kobie's health, he needs a "comfort zone" to call his own ~ maybe a room in your house that Thurston doesn't go into that can be set up with everything Kobie needs?
As for Thurston & Moxie ~ I would suggest that you try the rewarding with highly palatable treats in each other's presence. Try to establish more of a bond with Thurston by giving him a bit of individual attention & doing anything that makes him purr ~ grooming, petting, hand-feeding? It need only be for 5 mins at a time several times a day.
I would think that Thurston's early experiences with dogs must have been extremely frightening for him ~ if you are a cat, being dangled above a dog would probably be terrifying & as there was no escape, poor Thurston had no choice but to react with aggression! It can't have done much for his view of dogs so now poor Moxie's taking the brunt of it.
The best way to deal with any signs of discomfort between your pets is to try to stop them before it develops into any overt aggression. With cats it usually starts with staring, tense muscles, wide eyes. Cats that are feeling anxious have "closed" body language, sit hunched up, with paws tucked under them, tail curled tightly round their body, head sunk into neck. Confident & happy cats are more likely to have "open" body language, sit more upright, or walk towards you with upright tail in greeting, or the tail is in a "loopy J" position showing they are confident & relaxed. So maybe watch for these signs in Kobie & Thurston to give you an idea of how they are feeling.
If you detect signs of conflict, try to distract/remove from each other by calling Thurston towards you & away from Moxie or Kobie ~cats generally respond better to high-pitched, happy, upbeat voices, so no shouting, growling or deep voices. I understand that it is difficult for your mother to intervene, but if she can train Thurston to come towards her (the same as you'd teach a dog a recall using food rewards) then this may be an option. It may be more difficult in Moxie's presence as no doubt Moxie will respond if there's food on offer
but possibly throw Moxie's treat away from her & give Thurston a treat from her hand, or drop it on the floor nearby. Water pistols, rattleboxes, any sudden loud noises are very unlikely to have the intended effect on Thurston ~ if he's already feeling stressed & under pressure, this will only make it worse & possibly feel he has to up the ante to secure the resources he feels he needs.
As for time out ~ I don't honestly think that Thurston will understand this. Dogs are social creatures so removing them from social contact will be a form of punishment & maybe they will learn from this. Cats don't learn from punishment & they don't necessarily need social contact, so all Thurston may learn is that sometimes you shut him away ~ but I doubt he will associate the time out with his own actions. But there's nothing wrong with removing one or both of the cats from a conflict situation ~ you just have to make this avoidance of conflict into a happy & rewarding experience. So maybe remove Kobie to his comfort zone but then stay with him for a few minutes, settle him down in a warm bed, fuss him, offer food treats etc. Make going to this place a pleasurable experience.
I would caution the use of laser toys or anything else that invokes predatory behaviour in the cats ~ because this is all it is, & the physiology that goes with predatory behaviour is not conducive to new learning or being quiet & relaxed. There's nothing wrong with play behaviour or teaching mentally stimulating things to a cat, but without fast predatory play.
Another thing you could do with Thurston is clicker training. If you are interested in clicker training cats, let me know & I can send you a fact sheet on how to do it. It can work very well with cats ~ if you google cats & clicker training & Karen Pryor, you'll probably be able to find some footage of cats going around small agility courses
. It can be a great thing to build up postive relationships with cats, & provide mental stimulation.
I hope this helps but feel free to ask any questions anytime ~ I'm happy to help if I can.