Mother in law drama

My mother in law has stepped over the line.

I have 2 children with my husband and my mother in law has always had something to say about the things we do. Both of my children are teenagers and so they sometimes get an attitude with me and I get one back. I refuse to allow them to treat me badly. Well my son got upset and yelled at me as he was walking away. He told me to “shut the * up”. Then he went upstairs and started texting her and even though she didn’t know the whole story she told him he could come live with them. These are my children and they will not be going there. She doesn’t understand that she is making things worse for us, and it isn’t any of her business what goes on in the house. Am I wrong to keep my kids and myself away until she fully understands boundaries??

Please help!