OP, you've got another thread where your DD is having sleep problems too, am I right?
If so, no wonder the pair of you are all over the place, having to run round dealing with that deadbeat ex who's trying to get you both at his beck and call.
On the assumption that it is your DD that's having sleep problems, here's my tuppence:
Severly limit the amount of contact he can have with DD until such time as he can properly commit to that level of contact. Eg 3 - 4 hours one day each weekend.
She's very young still, and unless he can give consistent contact to her, then I fear that anything you do for her sleep problems will be undone by his twatting her (and you) about.
Ditch him having overnights.
At least until her sleep problems are alleviated and good sleep patterns / habits are established.
Is there a Dad's group on a Saturday or Sunday that he could have the contact at? Somewhere you can hand over DD to him, there's other people and kids around, and plenty of things for DD to do?
Perhaps find a Dad's group half way between you if he lives a really long way away, but bear in mind a court order would say you only have to make DD available for contact. It would be a very rare order that said you have to take DD half way or even take her to her Dad - the court assumes (quite rightly imo) that the NRP should make an effort to come and get the child(ren).