Maybe if you have a basement, you could convince your mom if you could do it there. I had a similar problem with my mom, she didn't want the guinea pigs living where "people" live, so I had to make them live down there. Just make sure your basement is safe, like no drafts and right temperature. You will probably have to block off a lot of parts if it is not a finished basement. Make sure you don't confuse basement with a garage!
Go here to make sure your basement is "pig proof":
http://www.guineapigcages.com/location.htm