Why can't you save your own money? I mean.. why should your parents pay for something they don't even like? You may impress them with your maturity if you tell them you will pay for everything yourself, as well as care for it completely yourself.

As far as convincing your mom.. if you agree not to ever make her so much as look at the snake, you may have some luck. Consider feeding the snake frozen/thawed mice/rats anyway. Then there will be no live rodents in the house, and the only time they'd be there is the day you feed the snake (assuming you have a pet store that sells frozen rodents)

Cali kings and BPs are both awesome.. as are ETB's.. but tree boas are certainly not a beginner's snake.. plus that they are EXPENSIVE.

Good luck.