It sounds like you need to work on your communication with your mother. If you talk to her without losing your temper, then she cannot accuse you of losing your temper. I get that mothers are good at pushing buttons, but you cannot let her get to you like that.
Choose a time that you are not stressed or rushed and sit down and have a conversation. Prepare what you have to say and do not let her get off track with emotional issues.
You: Mom, I need to set some rules of you are to continue to live with me. You are welcome to engage in the preaching work, but not in my neighborhood.
Mom: I'm your mother, Its my right to preach, you are being mean.
You: I respect you as my mother, but you are living in my house, and those are the rules here. Do you want to continue to live here or not?
Mom: You have to let me live here, I'm you mother.
You: No I don't. Those are the rules, do you want to live by my rules or not? It's up to you, but otherwise you will have to find a new place to live.
Mom: I'm going to call the elders, you are being unreasonable.
You: I suggest you do call them. They will agree that as the head of the house I have the right to set the rules, and that they don't actually allow cart witnessing at residential homes anyway.
Mom: You would kick your own mother out?
You. As I said, it's your choice to live by the rules or not. I am not preventing you from preaching, you simply have to agree to preach elsewhere. You are the one making the problem, not me.
Mom. So you are ashamed of your religion? You are ashamed of me?
You. Of course I am not ashamed of you. But it doesn't matter what my reasons are, it's my house and my rules, do you want to live by my rules or not?
You get the idea. No matter what your mother does, keep turning the conversation back to this simple point, it's your house and your rules. If you refuse to get drawn into the drama and stick to your point there isn't a lot she can do, you hold the power because you are paying the rent. Let her storm off and slam the door or cry, don't placate her or give in. If she starts preaching again, calmly sit her down and have the whole conversation again. Eventually she will see it's not worth the effort and give in.
It may seem like a lot of effort, but if she is like this with this issue she will be like this with other issues. It's better to set the rules and stick with them now.