I also keep my rabbits in the garage connected to my house, and I had the same issue. What I did was I would just have them run around in the room for 5 minutes, the next time 8, then 10, and I kept doing that until my mom saw it was ok for them to run around for an hour or so. Also what I do is I have a small cage/carrier that they can go in when they are done playing. Until I put them away in the big cage. Hope this helps!

Yes I think a gradual approach would be a good one (for the buns and your mom!). Maybe start with 5-10 minutes in a x-pen in the lounge: put in the fresh litterbox and promise to clean up any accidents. When your mom sees that they are being good and will not poop and pee everywhere, you could gradually increase the time and space they are allowed inside If your mom is worried about the carpet I would start with them inside on a tarp or towel under the play pen until they have proven themselves to be potty trained. You probably know they won’t wee everywhere but hopefully that would bring your mom peace of mind!

Agree with both previous posters but wanted to add that maybe promise to clean up any messes as they happen, and maybe offer to do a bit of extra cleaning as well, like vacuum the lounge when you’re done playing with bun. Then she won’t worry about the mess, and associate the buns playing with her getting a clean lounge

If all else fails, give her the sad face and turn on the water works .