Snickie's cats have issues

So I have three cats and a dog at home (I'm away for college but I'm close enough to come home for the weekends). We have:

Snick
- a fat black part Maine coon female, will be 9 in November. She's 17lbs, has medium-length fur, is a bit of a b****, and is decidedly my cat. She loves my parents too, but she loves me. We got her when she was about 10-11 weeks old.

Stella
- a black and tan dapple tween dachshund (mother was a mini, father was a full-size) female. She's 7 years old and just wants to play with all the other cats unless food is involved.

Ninja
- a chocolate point applehead Siamese male. He's 6 now and weighs about 12lb. He was a stray wandering around in Celebration (rich community near DisneyWorld), and one of my mom's coworkers found him, and when nobody claimed him, we took him. He's soooo personable. His favorite person is my dad. I think. He loves all of us really.

Aja
- a chocolate point Siamese female. We think she's a year old. We got her in mid-May. She weighed about 8.5lb then and weighs about 8.5lb now. She is most definitely my mom's cat. Without a doubt. On the weekends, she will plant herself on my mom's lap and will follow her around whenever she has to get up for one reason or another, and as soon as she sits down again she's back on her lap.

We love our cats. Unfortunately for Stella, we're not really dog people (she was an experiment to see if we could be dog people), but she's treated well.

So when we adopted Aja, we kept her separate from the other two cats initially, especially as we were waiting for her test results to come back from the vet for things like feline leukemia, worms, etc etc. They were all negative. Anyway, we started introducing her to the other animals. It took a while but she eventually warmed up to Stella and Ninja.

Snick, however, hates her guts. They are both dominant female type cats. And while Aja has the advantage of street smarts, Snick has the advantage of size. Snick is always the aggressor, yet even after she attacks and they have to be separated, Aja comes prancing down the hall again in like five minutes.

Several times we've had injuries, and we almost lost part of Aja's tail because of it (she spent several weeks in a Cone of Shame and with a bandage around her tail... she managed to get the bandage off on the first night and the cone around her waist by the next day lol). So we keep them separate to keep them from fighting. The barrier is a French door, and sometimes Snick will stare at Aja on the other side with pure hatred in her eyes.

One thing I wonder is if Snick is bitter somehow. We had another cat, Elizabeth, who was 19 when we put her down just days before we adopted Aja. Snick and Elizabeth were buddies. They would share a bed together (although it was more like Elizabeth would get the edge while fat Snick would take up like 90% of it lol). My mom couldn't be in the room when it happened. We buried her almost immediately because my mom wanted to get it over with, at the cost of not giving the other cats a chance to realize what had happened. We didn't plan on adopting another cat for a while, but then Aja showed up and we fell in love.

We're not about to give them up - my mom is completely enamored with Aja, and Snick is my baby. And it's been nearly four months now. Is it possible they'll ever stop fighting? Like, we don't care if they hate each other; we just don't want them to fight anymore.

Any ideas?
(No, we're not going to get the guy from My Cat From Hell to come out. He's in LA. We're on the East Coast. And it'd probably be really expensive anyway. lol)

Are Snick and Aja spayed? If not, it might help.

They are all fixed. We had Snick and Stella spayed, and Ninja and Aja both came already neutered and spayed.

Oh, dear. Yes, I think there are psychological issues involved--jealousy, feeling threatened, fighting for dominance. I'm not sure what to suggest, though. Maybe your vet will have some ideas or can direct you to some resource that can help.