I'm not sure her invite was for YOU. My guess is it was for HER. She is feeling guilty and she wants to show her kids that she is still a wonderful mom that is "doing the right thing". I bet she tells the OM all about it...."Tom, I invited Roger over for dinner. It was so good for the kids to see us all eating together and that we are ok. They need to see we are all ok and they will be ok. D6 even mentioned your name and we just went on. Kids are so resiliant and they will see that this was for the best."
My wife used almost EXACTLY THESE SAME WORDS with her boyfriend last summer. I know, because I recorded her, and I HEARD them.