I would have to go back and read your whole sitch (I have been dropping in from time to time, though)--you say he is not in Daddy mode. How has he demonstrated this? If he is not in daddy mode, do you think he will still want to be picking up your D? Are those days that he is scheduled to visit with her?
If at all possible, I would try to encourage a R between H and your D, but only if it is safe. We have to put our own pride on the back-burner. Also, most schools have resources for kids going through their parents Sep/Div. Let the teacher or school guidance dept know; they may even have lunch-bunch groups for kids to talk to each other who are also going through this.
This is one of the issues that you HAVE to talk to H about--if you are like me, it is best to keep it kids and business. I would NOT recommend doing the parenting course together if you are not both on the same page--the first time was VERY traumatic for me. I did get a little out of the second round, but most of it is common sense, and my background in teaching helps.