Hello, my name is Dr. Kara and I have over 20 years of experience as a veterinarian.
I am sorry to hear that Coco and Cuddles aren't getting along.
Cats don't live together normally in the wild. They have territories, although they are fluid, and will fight to preserve resources. In many cases with unlimited resources in a home environment and everyone is healthy they learn to live together peacefully and some learn to enjoy each other's company. But some cats simply never learn totolerate other cats in their environment or they may start to pick on a housemate if the housemate is sick. I know it seems cruel to pick on another animal that is sick but it makes sense when considering survival to drive a sick animal away so that the healthy animal doesn't catch whatever the sick animal has, and the sick animal isn't a drain on resources.
Given that Cuddles is vomiting and not eating well I think she needs a veterinary visit to make sure she is healthy, and to get her healthy if she is sick before we attempt to try and get them to get along again.
Do they ever ignore one another and co-exist peacefully while in the same room ordoes Coco react every time she sees Cuddles?
At this point I would never leave the two of them alone together when you aren'taround to mediate. And in fact you may want to start all over with introducingthem again once we get Cuddles healthy.
In aggression cases I recommend using a product called Feliway. I know it seems less helpful then it was but that may be because Cuddles isn't feeling well.
There are also pheromone collars which may help calm them both. It's worth a try. See this link: http://www.amazon.com/s/ref=nb_sb_ss_i_1_17?url=search-alias%3Daps&field-keywords=feline+pheromone+collar&sprefix=feline+pheromone+%2Caps%2C197&rh=i%3Aaps%2Ck%3Afeline+pheromone+collar&ajr=0
If Cuddles is healthy or once she is well again continue keeping them completely separated, behind closed doors for several weeks. That way they aren't constantly confronting one another but are able smell and hear one another and get used to having each other around in a non-threatening manner.Make sure to frequently switch bowls, beds, toys and use the same brush on bothcats to get them smelling the same and familiar to each other. Of course don't switch things if Cuddles has something contagious.
If things are going well then try using a large baby gate between areas to keep them separated from each other but able to see one another for a few weeks. If Coco is becoming aggressive at that point and picking on Cuddles then you may want to try ahomeopathic calming oral medication called Bach's Rescue Remedy. See this linkfor further information: http://www.bachflower.com/rescue-remedy-pet/
We want them calm enough to learn to at least co-exist.
If things are going well allow them in a room together, but only when you arepresent.
You should make sure that there are plenty of spots for both cats to get up and away from eh other, such as cat trees or ledges that are carpeted and comfy to sleep on. Cats do tend to get along better when resources are unlimited. Make sure there areplenty of toys for everyone and don't let Coco harass Cuddles. If she isn't respecting her and does chase her or continually tries to approach her aggressively it's fine to use a can of coins to throw near her as she approaches her for negativereinforcement.
You may also want to feed them separately in different rooms so neither feels thereis any food competition if that seems to be a sticking point.
If Cuddles is healthy and all else fails discuss anti-anxiety meds with your veterinarian like Buspirone or Amitriptyline for both of them as stress is certainly playing a part in this. If either one hates taking pills there are transdermal gel formulations of these medications available.
Finally Coco may do better when allowed to go out so you may wish to construct an outdoor cat pen so she can safely spend time outside. Here are some examples:
Best of luck with this situation, and let me know if you have any further questions.