Heather, I am keeping you and your daughter in my prayers today. I pray that everything will be okay and he will act civil upon arrival.
Please stop trying to figure out the why's of this visit and his insistence to take her to lunch. There could be any number of reasons for this...but you may not find out until after he leaves, if he manages to get her to go w/him.
Stay cool, calm and collected. Don't let him ruffle your feathers.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.