BunBun appears to be staying. My daughter likes her and she likes my daughter. She comes running whenever anyone enters my daughters room (it doesn't hurt that we usually enter with some freshly washed greens!) She is a big fan of neck massages and does a great "flat bunny" when she's really into it.
Litter box training is continuing slowly. Very slowly. Inside her ex-pen she's golden. She always uses the box in the corner beside her cage/bed. But when we let her out to roam she will go *beside* the litter box I have out. So we are not completely set yet, but we are in process. We have time. I think we will get there.
Once we have out car fixed (hurm......) I will set her up to get neutered. That may have an effect on the peeing as well. Might not, though. She's already a year and a half and she has her habits. But it will be better for her health so we will do it even though she's an "only bunny".
She is very pleasant and none of us are scared of her anymore though we all do respect her! That is probably for the best. Someday I may try to pick her up but we are defiinltely not there yet! The cats are still fascinated and have only interacted with her through a baby gate or through a baby gate and an ex-pen. I don't know if they we ever interact without a barrier there. Better safe than sorry I think on this one. And we are in no rush.
This is a very nice thing for my eldest daughter and I'm really tickled that it's working. There was a time there where the bunny and my daughter were getting along great but I was still scared of the bunny but very thankful for her presence. Now we have a careful friendship. As long as she makes my girl happy, she's a golden bunny in my eyes. No matter where she pees.