You have to let your mother-in-law come visit.
You do your best to control your temper. You be polite. You be considerate. You don't argue. Remember: This is a temporary situation. She will leave. Maybe not soon enough for you, but she will leave.
Parent in-laws are hard people to get along with. Once your kids grow up and get married, you'll see their spouses and won't approve. After all, your children are the best. They're princesses. They're bright and talented. Whoever they marry won't be good enough for you either. This is your Mother-in-law's world. Her princess married you. What a disappointment when she could have married that really nice boy, Prince William III of Luxembourg.
What about the children? They will learn from your encounter. They will learn that you treat your parents (even in-laws) with respect. That you control your emotions. That you sometimes have to put up with very difficult people. (And, yes. They will see your mother-in-law as a very difficult person.)
And your mother-in-law will sooner or later learn that you're not such a bad guy because no matter what she says, you treat her with kindness. Sure, you're no Prince William III of Luxembourg, but you're not as bad as she first thought.
I have a very difficult father-in-law who was not happy with me. By every one of his criteria, I was wrong for his daughter. I learned to control my temper around him. I learned not to argue with him. I kept my mouth shut. I smiled.
It took over a decade, but he learned to respect me. He learned that his daughter truly loves me and I love his daughter. He learned that I might not have raised my kids the way he would have, but he sees they turned out okay in the end, and that my kids love me and I love my kids.
Talking about difficult, my mom is a very difficult person, and my wife had the same issue with her as I had with my father-in-law. I gave her the same advice. Be kind. Be nice, and the relationship will improve. Remember, if my mom is combative and argumentative. It's her fault and not yours. You've been polite and kind. She's the one with the problem.
And things did improve. We visit my mom, and my mom comes and visits us. My house isn't up to my mom's cleanliness standards. My wife's cooking isn't up to my mom's standard. My mom will occasionally role her eyes, but she gets along with my wife.
By the way, your wife can help too. When my mom and my wife were not getting along, I kept reminding my mom that I love my wife, and I'm not going to divorce her, and for my sake, please try to get along with her. When my mom said nasty things about my wife, I reminded her that this is my wife, I love her, and please don't say those type of things to me because it hurts me.
When I was having problems with my father-in-law, my wife told him the same thing. I'm her husband.
I wish there would be an easier way. You can't demand to your wife that her mother can't visit. Your wife loves her mother. Be aware that your kids know the situation and exactly what's going on. They may like the sweets and the presents, but when your mother-in-law disrespects you, they know who's not playing nice. Kids are a lot smarter than we think.
There's a reason why there are so many mother-in-law jokes and cartoons. You're not alone. I hate to tell you that it may take years, and even after that, it will be a shaky détente. However, for your wife's sake, do your best to get along. Remember that the problem is your mother-in-law and not you. If you keep that in mind, your wife and your children will also see that too.