Personally, I hate people that are late. Now valid excuses are fine, life can be chaos, but if your one of those people that are late every (other) day by 5 -10 min then I have no sympathy for you. Its time to grow up, show some respect, and do your job. It sounds like you should have taken the job more seriously. Sure you can find a new job, but it sucks being on the bottom.
I'm not sure what your major is, but having 4+ years of work at a bank looks good on a resume, it looks even better if you?re trying to get a position from the same company once you graduate. If you where a teller, then that?s even better, having years of customer interaction is always a plus.
On the other hand, your 19. You?ll be fine, you?re just getting started. One day you will look back on this and laugh. Is your mom being overly mean? She probably is overreacting. She?s just trying to ?help? you.