People don’t have to scream at each other when they disagree. Your mother apparently hasn’t learned how to deal effectively with conflict. You haven’t either. Both of you are at fault at this point. Neither of you knows how to talk so the other will listen or listen so the other can talk sensibly.
The alternative to fighting isn’t to just back down. That’s just another form of the fight. The two of you need to learn how to deal respectfully with each other — and probably with other people — when you need to negotiate something.
I suggest two things: There’s a great book called Getting to Yes: Negotiating Agreement Without Giving In by Roger Fisher and William L. Ury. You and your mom could read it together and talk about it. Try out the strategies it suggests.
If you can’t come to a new way to deal with your differences on your own, then make an appointment with a family therapist with the goal of learning that skill. It will help the two of you have a better relationship. Even more important, it will help you have a better relationship with your partner and children some day.
I wish you well.