Since your parents aren’t paying the bills, you’ll have a harder time since they don’t have any skin in the game, only you do. I would suggest having a vet appointment and bring your mom there and have the vet explain why inside is way safer than outside (for many reasons). Back then, people didn’t think bunnies were pets, only food, so they didn’t learn that bunnies should be kept inside like dogs and cats should and how bunny care has tremendously gotten better and she only knows what she knows from back then, which wasn’t the care we give them now.

You can also do research and put together info on why buns should live inside. She might think what you’re saying is false and that “she knows better” so having a vet tell her is what I think would help you since they have the info

As long as they are in spacious housing that is very regularly cleaned, protected from the elements, and are played with a lot, rabbits can be great outside. The reason outside bunnies get a bad rap is because of owners who get lazy and forget to clean out the hutches or play with them; thats when you end up with sick, sad rabbits. Its not outside that is a problem, its careless owners. It is more convenient to provide good care for a rabbit when it is inside (the closer the bunny is, the more likely you are to take good care of it). But if you are willing to work, you can keep outside bunnies as healthy and happy as their indoor counterparts.

I also have two bunnies and I was in a similar situation. Lily and Cocoa were outside bunnies and they were played with a lot, their hutch was regularly clean, and they were protected from the elements. They got mites, intestinal parasites, multiple cases of gi stasis, and Lily has megacolon. They were out there for a year before we found an amazing vet who convinced my parent that they need to be inside and was finally able to diagnose Lily. My parents had rabbits when they were teens so they took a lot of convincing. I know how difficult it can be, good luck!

Have you asked what specific reasons your mum doesn’t want them inside? Is it just that she thinks that they’re happier outside? Or does she think they’ll be smelly, noisy, destructive etc?

If you can find out what her objections are, then it’s easier to persuade her as you know what you’re up against!

For example, if she doesn’t want them inside because she thinks they’ll smell, you can offer to clean out their litter trays every day or have them in your bedroom.

You could also point out that it’s actually not very good for bunnies to be being moved between indoors and outdoors – the heat of being inside means that they don’t grow thick fur for the cold outside when they do go outside. (This could be risky and end up with them being permanently outdoors… But really, it would be best if they’re going to be outdoors to be permanently outdoors so that they grow a suitable coat).

My parents didn’t want the rabbit completely inside either, so what I did was I completely rabbit-proofed my room, and asked them to give me just two weeks, and if they had any complaints about her running around in my room I would make other arrangements.
It’s been months now, and since she’s litterbox trained and stays in my room, they have nothing they can complain about and everybody’s happy