If the pounds are full it's your mother's responsibility to make sure the kitties have homes. It's not right to dump them, and I can't believe she would even consider it. It's also against the law. You'd better believe if my own mother did that I'd report her in a second. I'm sorry you had to be put in this uncomfortable situation, but there are alternatives... ACAT, for instance, will takes in cats, pay for medical costs (including surgery) and adopt out kitties. They don't euthanize, either.
If she doesn't have the money to spay or neuter her cats, tell her that there are places that will do it at little or NO cost. I have two male cats that were neutered absolutely 100% free. I never paid a penny for it.
Good luck, and keep us posted!