Cat becoming very agressive

My cat Pepper just turned 2 years old. I rescued her from the local shelter when she was about 9 weeks old......she had been dumped by the side of the road with her two sisters. At the time when I adopted her, I had one male cat (who passed away last May). A few weeks after adopting Pepper, I adopted Woody (who passed away in March). Last July, I adopted Isabelle....a 4 month old (at the time) kitten.....who is now just over a year old. I was also fostering two kittens when I adopted Isabelle. About two or three weeks after I adopted Isabelle, Pepper began to hiss and growl at Isabelle....and would attempt to attack. Now, the attacks are becoming increasingly worse and more frequent. Both cats will be playing at opposite ends of the room and Pepper will suddenly fly at Isabelle, attacking her. Or Pepper will be in another room and will literally run as fast as she can and jump on top of Isabelle.
She is also agressive towards Angel, the momma cat that I am fostering, but she is very rarely around Angel. If Pepper sees one of Angel's kittens, she begins to growl and hiss. Pepper will also attempt to attack the dogs on occasion.
Once in a while, she will also attempt to attack a human but this doesn't happen very often. Usually she is a very loving cat, but there are times when she will growl and hiss if I approach her.
I have talked to a vet, who has no clue why Pepper would be doing this. I am afraid that Pepper will end up needing to be put down because it seems as if she is going crazy....because the agression is not all the time, it's like something snaps inside of her head and she goes nuts.
Does anyone have any suggestions for me? By the way, yes they are spayed.

So you brought a new cat and a foster cat with kittens home at the same time?? That is a lot for any cat to adapt to. I'm fostering a mom cat and her kittens and I have them in a separate room. My cats are not allowed to interact with the foster family at all....especially since the mom cat came from a shelter and we don't know what she could be a carrier of. I wouldn't put the cat down...I would rehome her...but first, I would try Feliway (which you can find at PetSmarts).

http://www.catfaeries.com/feliway.html

Katie

Yes, she's been seen by the vet. She is healthy, and the vet has no idea what may be causing the agression. The only thing he could say is, maybe she has a mental problem.