Yes you were. It's good that you provided some background, because it's clear that you don't like him and tend to provoke him. You seem to expect him to do things for you (driving lessons etc), which he has no obligation to do. Calling him names in front of your mother is also wrong. I'm sure she felt terrible.
You keep using the word "harassing", but from his point of you, you've been harassing him instead. You need to grow a thicker skin and ignore insults. Verbal abuse does not give you the right to keep beating up a person.
I don't know how old you are, but I suggest you either move in with your sisters or if you're old enough to get a place on your own. Your mother and her bf don't owe you anything.








