Yep, mom rules all unfortunately :(
But, maybe you and your mom can come to an agreement of some sort? Have you seen a lot of other cats around? In my area, we have a few, but only two come around my house, and I've been feeding them for years.
I try to feed the others but I think the big momma kitty I feed has marked my house her territory, the only other kitty that wanted to come around was tiny (not her baby or anything) and didn't know any better. She grew attached to them, so they both stay around.
HERE though, in the winters, it's brutal, so they will try to crawl INTO the cars for warmth. I started taking boxes (I get a lot of shipping boxes), wrapping them twice in saran wrap and duct-tape to seal off ALL open edges. After that, I find the clothes i'd toss anyway, and shove a couple in there, eventually the cat will bring what they need in there. I check them about once a day in the winter to make sure no snow has really gotten in there (and leave them out in the summer too).
The boxes last quite a while as long as you saran wrap them up well, and the cats LOVE them. When I check the houses, I always sneak some extra food in there.
Maybe you guys could decide to feed her here and there, and if there's no other cats coming around, continue doing it?
Or if you have no other pets, and your mothers only concern is other strays.. you could give her food, water, and some material to sleep in in your shed/garage... eventually she'd likely come around to you guys. If you try/want to bond with her, definitely use your own clothes, even if it's something you were going to throw out.. wear it for a day. Your scent will stick to it, and she'll grow to be comfortable with you.
Sorry for the huge writeup! Good luck to you and that little kitty :)