Start with a pair bearded dragons. Let your mum get used to having reptiles in the house. Join one of the herpetological societies and get your mum to take you to the meetings. After a while, she'll start to get interested and want to learn about the various animals out there. She'll get the chance to touch and see reptiles and talk to other people. With luck, she'll relax a bit, and you might get that snake. She might actually buy one for herself before you get one of your own.
Anyway, that's what happened in my house and I'm the mother in question.