Research the subject and take her to the pet store and show that there are cages that are almost impossible to get out of(if used right) Educate your mom about the subject. Show her there is nothing to fear about a harmless snake. Have her hold a snake at the pet store have her ask her questions and get them answered. Knowledge is power. When she holds the knowledge about the animal you want she should ease up and let you get your first snake.
Show her just don't tell her. Get people that know about the subject to answer her questions. This will help you out alot!