Maybe I’m just grumpy today, but I want to take a step back regarding your situation. I have had many apartments, and ALL of them allowed my bunny. First, I tell them that s/he is in an enclosed cage. Next, I tell them that bunnies are silent. The two main concerns are damage to their property (and you never let them know that the bunny comes out to wander around and play) and noise bothering the neighbors. Both are moot in the case of a rabbit. So I’d ask your sister-in-law to check with her new landlord specifically before she gives up her responsibility. Now, if she’s just farming it off because she’s…well, the bunny needs a new home.
In your case, you’re looking at years of living with allergies both of you have right in your home. I can’t abide allergies right under my nose (sorry) so before the bunny becomes used to you, I would work on finding a new and happy home. Adults are better than children, so ask around at where you work and socialize and see if anyone (no homes with dogs already, please) will take it. Also, check out your local rescue for adoption. You could be a foster home while they put out a call and do screenings, so you don’t have to give up the bunny to the shelter, but I think you need to think it through more – something your sister-in-law did not do.