"She started of by asking if I was busy. I didn’t answer but asked what was up. Then she stated that she had some practical’s we needed to discuss."

You answered that very well.

"Then she told me something about D6 getting a new book at school already and then some about her….she just babbled.
(At this point my head started working because I was in doubt if babbling about the children should be stopped or not. Since I like to know what goes on in their lives I just listened and made these small listening-sounds like oh, yes, hmmm and so on)"

I understand, you are interested in their daily lives. You may need to think of a tactful way to have W stop her babbling and get on with practicals. Like you said, she will do this again. One problem LBH's have is not being prepared with what to say. You need to think of possible things she might surprise you with in the upcoming months, and know ahead how you will handle it. Practice what you will say, if it will help you remember and be able to sound confident.

"Then she shifted towards D4 being sad and asking her why her and I can’t live together. She had told D4 that we weren’t very good at living together. I left this uncommented. She talked a little about this and also about D6 not talking about this but listening a lot.
Then shifted towards D4 asking her if I could join them for dinner and she invited me. I left it unanswered but she kept on asking so I told her that I didn’t feel like doing this."

You handled it well. But when you say, "I don't feel like doing this" or "I don't feel like being friends"........it sounds as if you are acting as if your feelings are hurt and you are reacting. You need to direct it back to her decision. Don't take responsibility for D4's sadness. Yes, you co-parent, but she has to deal with certain things as a single parent b/c she chose to take the children and leave their home. She thinks you will come to her rescue to help her deal with the sad outcome (having to explain to her girls why she doesn't live with daddy any longer). I strongly feel that the parent who made the decision to break up the family should face the unpleasant ordeal of answering questions the little ones ask them.

You were very good not to jump in with a bunch of comfort words for her. I don't believe she should be validated b/c she needs to see this is a result of her choices and you will not make her feel better about something you did not want. See what I mean? I would speak softly and say, "But this is what you wanted. Surely you knew you would have to deal with these issues."

She may storm off, saying something like, "I should have known I could not count on you to be there when I need you!". (or something similar). Be prepared for it and don't react. Say good-bye and let her have her pity party. She thought she could leave you and still have all the benefits of the R. She is not going to like when she finds out it does not work that way.

Good job.

P.S. You will have your part in dealing with the kids issues when they are at your house. But she will probably have the most, as she should. Don't take her guilt or responsibility away from her.

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!