We had a rabbit for 6 years they are great pets and can be litter box trained. Ours lived in a cage in the house. I also have two dogs and two cats at the same time. (rabbit died of old age I guess) It is possible for them to become friends but you'd have to patient and they could not be left unsupervised. If you must get rid of the rabbit. Check you area for rabbit rescues they can possible help. Also, some ASPCA (animal shelters take them) make sure it is a no kill. However, many have been there for years at my local ASPCA. Good Luck. I hope you decide to try to keep the bunny.
Also, if you choose to get rid of it, you can be anal about your screening process. Ask the potential buyers questions like if they've own rabbits before and how long they lived. Ask the buyers anything important to you, such as if they use litter training techniques or let the rabbits run free, or use cages or not. If they use litter training techniques it may indicate that they let the rabbit have play time outside of a cage, which may be useful knowledge to you. You can be as judgemental or picky as you feel is necessary to place your mind at ease, before handing your bunny over to someone else.
Try asking the vets office to post notes on their board. You can also take her to your local aspca or animal shelter