I'm sorry. Any old excuse will do for your h as to why he left you.

So, he wants to keep some distance from you and yet, he asks you about walking down the stairs, pointed out his new car, had lunch w/you and your family and yes, even taking you to the school...doesn't sound like distance to me...his words don't match his actions.

I would respect his decision about the distance issue and go as dim as you can w/him. He still doesn't appear to know what he wants in the way of communicating w/you.

Try to keep the focus on you and your child as much as possible. The holidays are fast approaching and your attention will need to be on her and making new traditions for the holidays for the both of you.

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.