Tough... do you need to fill that spot if she leaves? How quickly do you seem to fill spaces, usually? This may be a determining factor, as in "a bird in the hand is worth two in the bush"?
I agree that this will likely end up in more issues for you. Perhaps, if you are concerned about filling the spot, do another short term contract. HOWEVER: I would lay the smack-down (lol) about the lateness and the cheques. Let them know that late pick-ups will not be tolerated, and that if something comes up you MUST be notified. Failure to comply will result in immediate termination. What, no 411 or phone books in the area dad was in?? Come ON. Even if he didn't have your number (which he should have!!!).... please. And I would not allow them to come if they don't drop off a number of cheques equal to the contract care dates. No money, no care. I HATE chasing people down for money.
It doesn't sound like you have an issue with the child, or else I would say tell them to take a hike. Maybe if you get a little hard-nosed with the parents, the working relationship will improve.