Well..my situation was kind of similar to that. My mom hates snakes and thinks they are disgusting, slimy, dirty, evil creatures. My dad didn't really care either way but he pretty much said, "If your mom says no, then I say no too." My brother also hates snakes but he couldn't care less since he's at college most of the time.
Eventually I struck up a kind of deal with my mom. For one school quarter, I slaved away, doing dishes, folding laundry, keeping my room immaculate, studying like the dickens, cleaning up after my bird, practicing piano 2 hours a day, not watching tv, etc. AND I got all A+'s in school except in Math (I got an A-) that quarter. Well, she really couldn't complain so my brother drove me to Westchester and I picked out my lovely snake and bought everything else (including 100 pinkie mice) and came home.
One small detail that my mom didn't really realize was that snakes eat mice. She thought there was some type of special snake food or something, I don't know. Well, if there is one thing she hates more than a snake, it's a mouse. Anyway, I finally convinced her that no "germs" would be able to escape through 3 layers of plastic bags all encased in a plastic tupperware container and she puts up with it to this day. She still refuses to watch a feeding (She goes into her room and locks the door) but my dad thinks it's really cool and my brother actually fed him once.
Well while I was rambling here I see kellum has created a much more useful (and concise) post than I, so definitely follow that link and read everything. I found it AFTER I'd already slaved away.
Good luck convincing your mom! Corn snakes really do make great pets.