I'm sorry to hear that, perhaps you can politely try to convince her with facts about how it is bad for the bunny? Perhaps you already have--but some reasons I thought of that I didn't see mentioned where:
When the garage is closed, there will be poor ventilation (even with a fan) that will (as others said) make it hotter for the rabbits and with not as good air flow, I can imagine it's possible they could stink more.
Do you guys keep cars in the garage? Because if you do, I would worry about my rabbits being exposed constantly to fumes. Or, if you keep power tools in there, again I would worry about gas fumes.
An outdoor hutch may be a bit farther than the garage, but ultimately the rabbits will be happier out there. They can enjoy the weather and outdoors properly like in nature. Plus, a hutch can easily be made predator proof and I know I and others have successfully and safely kept our rabbits outdoors for years with no issues.
Rabbits get used to loud noises and chance sightings of predators as well. Lots of people worry about them being scared to death (like with a heart attack) when startled, but to me I've never really heard anyone actually use real life examples of that happening (at least very often). My rabbits got used to power tools and other crazy sounds without batting an eye. They also had a completely closed-in area of their hutch they could run to if they ever felt the need to hide. (And sometimes they did! But were okay)
Properly provide for them with good housing and other needs (especially depending on the season) and your rabbits will be set up for success. My bunny loves to sit out in rainstorms (in the uncovered part of his hutch) and mine have made it through many different kinds of weather (hot, cold, stormy) with no issues. We've even had plenty of visitors from predators like raccoons and possums and now our stray kitties we adopted and my rabbits never batted an eye over them. Sure, I'm not saying startles from predators trying to get in can't happen, because they can, but I think if you give them a good, proper, sturdy hutch/cage you wouldn't have to worry too much.
Those are my experiences, at least. I know some of this overlaps with what others have already said (and what I presume you've told your mom) but hopefully I have offered more that might help!
Lastly, unless you already have, it doesn't hurt to remind her that these are living creatures that have needs that should be met. You shouldn't put your needs/wants (like having them close) first before the safety and comfort/health of your animals. If you don't want an indoor pet, you'll have to deal with the fact that the animal has to stay outside, and that means making the effort to have to go out to see them and care for them.
In my opinion, I love having my animals outside. It gives me a chance to get out of the house and get fresh air.
Wishing you all the best! Sorry for the lengthy post and hopefully I have been of some help.
