A couple thoughts on a few different sides...
I'm a parent now so I probably understand some issues here that I would not have before becoming a parent. First of all, just generally speaking, it is tough enough being a parent and trying to raise kids, manage a household, work, etc... So she deserves credit for doing a great job and also some leeway if she is not seeing things the way you are. She might just be thinking she has enough on her plate and the risk of something throwing daily life and routine off track is just not worth it. Especially for an animal she is not inclined to like.
So, first thing is to emphasize how easy snakes are to keep once you have the proper set up. You have done your research, you will probably be excellent at maintaining a happy snake. As a parent, I was not willing to add another mouth to our household 6 months ago but when I researched and realized how a snake would likely not negatively impact our daily routine I gave my daughter the green light.
Second, please think about the impact of taking a snake with you upon graduating from high school. I would not have purchased a snake if I was renting an apt. or home. Dealing with landlords and their approval or the thought of moving everything would have been a deal breaker.
Even in college, alot of friends got dogs as soon as they moved out of their dorms and then they could only rent from certain places or had to pay extra in rent or deposits and it was always an excuse to not get a good chunk of deposits back when they moved. Seriously, you will need to hold onto all the dollars you can over the next 10 years, at least, and you will hopefully have lots of new and unexpected opportunities come your way.
After college in Tallahassee I took a job in Atlanta and after two years received a job offer of a lifetime and moved to Manhattan. Apparently, you cannot have a python in Manhattan. So what would I have done if I had a BP then? You just don't know where life will take you and it doesn't sound like you can send your snake back to your mom like alot of kids did in college when they realized owning a dog was problematic.
Good luck to you either way it works out!