well the first thing you will have to worry about is getting the cat to a vet. with that much extra weight there is a good chance that she has luxating patellas (this causes severe pain because the knees are popping out of place and can sometimes need surgery-my cat needs surgery for it and he's only 14 pounds). this is a very expensive surgery (vet gave me an estimate of around $1200 for my cat and that's only one knee). this could be another reason why she has to drag herself...she's in pain. she may also have liver, kidney, or other internal damage from the excess weight too. you need to find out exactly what is going on. is it a health problem that is causing her to gain weight? something only a vet can tell you. you can guess its all from bad feeding, but it may not be or it may have started that way, but now she has health issues from the bad feeding. best to have it all checked out before stressing her out with your rabbit. she may not even have a strong enough heart to be able to deal with the rabbits annoyances to her. i agree she will probably be put down at the shelter because they don't wanna pay all that money to take care of medical problems, get her to lose weight, and get her healthy enough to adopt out. if all checks out well with the vet though and her heart, lungs, etc. are all okay then perhaps the rabbit annoyances won't be all bad. maybe the rabbit annoying her will cause her to move around more thus hopefully leading to weight loss, but like i said you don't wanna just stress her out. she's already stressed out from losing her owner, being forced to move to your neighbors, and now being forced into a new home potentially one with a rabbit and maybe other animals and new people. she needs to be put in a room by herself for a few days and slowly introduce her to the rest of the house and then the other animals after she is comfortable with the house and with you and your man.