I'm sorry to hear about your situation, but I think I kind of know how you feel. I'm not the only Christian in my house, but I'm the only one that has expresses it, and it causes trouble. My mother and I don't get along AT ALL either, and she has told me to leave if she doesn't like how she runs things. (The whole family is convinced she has anger issues, but she denies it.) I am fortunate though that I don't get stuck being a mother for my little brothers though. My family is quite functional overall.
Here's some of my advice. I hope it helps a bit. Feel free to message me if you need anything else!
Firstly: Pray, pray, pray. I see you're already doing that, which is very good. Bringing it all to God first and not letting anger, frustration, fear, etc. boil inside of us feels so much better. It is so easy to let those feelings get the best of us, and it causes us to sin and it makes the situation worse, overall.
I like the Corinthians verse Bea22 shared with you. It's a good one to keep in mind. Personally, I like reading Psalms when I'm stressed out about home.
Second: Make sure you have support from friends and other family around you in case you really feel the need to move out. If you haven't spoken to anyone over there about your situation at home, I would advise you find someone you trust and see if anything can be worked out. Always have a backup plan should anything go awry.
Third: I've noticed that with my mom, no matter how hard I try to convince her, I can't change her mind about anything--even when trying to explain the right vs. wrong thing to do. It causes more arguments and puts a lot of pressure on an already strained relationship. You, being the only Christian in the house, probably see and think about things a lot differently. I'm not saying that your mother doesn't have any clarity, but you have claimed Christ and your mind is being conformed to His. If our mothers are anything alike, getting her to realize the hurt she is causing usually doesn't go to well...
It good that you still do your best to respect your mother and serve your family. You have to do what you can to keep a measure of peace around the house. It is the right thing to do. Stay strong, and when God leads you to speak out, stand your ground and do so. Matthew 5:11-12 "Blessed are you when people insult you, persecute you and falsely say all kinds of evil against you because of me. Rejoice and be glad, because great is your reward in heave..." Looking at the other beatitudes is probably a good idea. They are a good reminder about how we should live and treat others.
No matter how hard we try, we can't convert people. Only God does that, and it is in God's own time. We are instruments of the Lord. We can be sowers of the seeds, but it is God that tills the ground and prepares the heart to be transformed and transforms it.
Fourth and finally: If and when things cool down between you two, sometimes simply sitting down and having a civil conversation resolves a few things. It's always worth a try.
I will keep you and your family in my prayers. Keep your head up, Andri'a. Surely, God will show you the way.
In Christ,
River