No, I would not accept the apology. I think a sincere apology face to face is in order here. You don't deserve anything less. I'm not saying you shouldn't be grateful for the card, but her not writing anything in it, kinda seems as if she's just throwing it at you to get her way.
Ask your husband to talk to her. It's his mother and his family after all. That makes it his job to confront them on these issues, not yours. It was a good thing for him to back you up that day. He should tell her how she should apologize to you. And if she refuses, well, then she shouldn't be allowed in your home. She must learn her place and respect you and your home whether she likes it or not. If I were your husband, I wouldn't speak to my mother until she apologized. His family, you and the children, come before any other relationship. But if that seems too harsh for you either one of you, he can visit her on his own time without having her come to the house.
Sorry you're in such a difficult position. In laws just don't seem to know their place sometimes. Which is why it's important to stand your ground, even if your husband is not behind you, which fortunately he is. Good luck.
