How can i regain my moms trust after making the same mistake over & over?

First I just want to say that I'm so sorry this is happening. I think your mom is just over reacting and very angry right now. I know for a fact she would not kick you out of her house. So don't worry about that. No mother would do that to a 13 year old. Maybe you need to ask someone you trust very much to ask her if you guys can talk in a calm manner. Then when she agrees, go in and apologize and try to work things out. I'm sure she will understand if you explain. Say that you will try really hard not to cry and ask for her forgiveness. If she says she needs time, that's ok. Everyone needs time to cool off. I promise this will at least help ok? I do this when I get in fights with my mom.