I'm angry at my friend's mom
Why do you have anger towards your friend's mom?
I just hate her, she's an annoying bitch.
If you dislike your friend's mom, you should still treat her with respect. First of all because she's an adult and you owe her respect, and second because she's your friend's mom and you could hurt your relationship with your friend if you hate his mom.
I don't think I should care about how I hurt my relationship with my friend.
It makes me wonder how serious the friendship is of you feel that way.   You should try to steer the both of you towards activities that do not involved being around their mom to help strengthen the friendship.