Hi, Febreezle. You’re in the right forum.
I can relate to your situation, and being mystified by it. First, I want to say that he is perfectly fine and is fine staying in the living room. He clearly prefers it, and now that you have him there he is very happy. I wouldn’t worry, especially since you did the right thing and had him checked by your vet. (btw, I encourage you to have him neutered for the sake of his health down the road. I digress.)
My last bunny, Sammykins, lived in my apt. for several years in an xpen with run of the apt. while I was at home with her. She always would go in and out of her pen when I let her out as long as the door was open, and often she settled in there without being coaxed back. She hated walking on tile also.
When she was almost 6 we moved into my parents’ house, and she had her xpen on an area rug on tile in the family room.
Once she was in my folks’ home, she stayed in her xpen. I would leave the door open, lay down a little area rug, but she didn’t want to come out. I carried her out to a bigger rug for exercise, but she got so definite about not leaving her xpen that I stopped closing the door entirely. She simply never came out. Now I know it was not good for her exercise health, but it was helpful for keeping her away from my Dad’s wheelchair, and she was clearly happy to have everyone in the room with her. She always hated being picked up anyway.
So, yes, I have heard of this.
The best explanation I can give is that: we see it as a cage, but they see it as their safe home. They are not trapped in a cage as much as they are comfortable in their private space. You are a guest when he lets you in, and like any welcome guest, you (your daughter) can join him for some pets and nap time. He knows that you understand it’s his territory, but none of us object to someone putting food in front of us or cleaning up after us, do we? Well, bunny slave, he has trained you well, and it’s a happy set up just the way he likes it. 