Most apartments we've talked to while looking for a place to move, are ok with reptiles because they're in tanks [or tubs or whatever] and can't just move around the apartment and stain the carpet. They basically place them under the same rule as fish and fish are covered by renter's insurance because if the tank breaks the renter's insurance covers the damages from the water leaking.
You need to have a sit down talk with your mom. Sounds like she's blowing you off. I know you love her and don't want to fight with her, but she needs to know what's going on and what's best for not only the snakes but also your sanity, because it sounds like this is stressing you out worrying about the snakes health and your mom fighting with you over this. She needs to make her concerns more apparent to you, and you need to inform her of the importance of having your snakes in proper, healthy environments.