According to what you've written, it sounds as if your W wants you to be available for her to vent about how her life [censored]. She's looking for a temporary band-aid to make her boo-boo feel better.
I have a feeling that OM doesn't put up with hearing all her woes. He's there for the good time only. So, she turns to you in her low moods, and to OM for the highs. Has she ever been diagnosed as bi-polar?
As for standing by her side during this time with the funeral, etc., I kind of think she'll let you know if she wants you with her or not. But as unstable is she is right now, and for the sake of your children....I think you should be available.
I think it's best to put any thoughts of R aside. You need to see her like you would see a sick patient. Don't make any rash decisions and don't let her talk you into anything. But if she takes a nose dive, somebody needs to get her to the hospital.
During the days that follow the funeral, somebody probably needs to keep close contact with her. Does her sister live close?
Tell me again the ages of your children, please. Why do you need to send TM back and forth about them?
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!