About the boys...my concern is if they see their dad going along quite often, they may think that the two of you will reunite...just don't know how your boys will digest this togetherness if it happens too frequently. Just my two cents.
I think Hopper has a good idea...take the boys out for treats, etc., for a while and then offer up an invitation to your h. He may or may not accept, but time will tell on that one.
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.