Did he tell her that HE noticed she is rude to you and she needs to stop. Or he told her that YOU are upset with how she talks. It’s a big difference. First option is acceptable way to address someone being rude to your spouse. Second way is throwing you under the bus and making you a bad guy. Why did he do it? Hopefully he meant well but he’s in a tough spot kind of. That’s his mother. He knows she is rude but his hands are tied and now there is more drama

Oh she doesn’t feel awful as she knows what’s the proper way to speak. And she knows how to speak to you without rudeness.

As about awkwardness, I think there must already be awkwardness in some ways as when you were divorcing you wrote to her about some negative things about her son. That’s maybe why she is rude to you. She might be resenting you. She’ll go back soon as no one has covid forever and it all be back to normal. Thankfully she doesn’t live with you. I doubt she’ll move in. Few more days. You can do it.