I would assume that the issues are not about your daycare but about the dad feeling like he has no control in the process and may be eliciting the info he wants to hear from his child by what he says to her.

Make sure that you treat each parent equally. While some things have to be on the same page make sure you speak to each one, give them copies of newsletters, daily reports whatever you do that they do not have to share with the other parent. The dad needs to be made to feel that he matters and can have some say in things and the whole daycare issue has not been railroaded onto him - he needs to feel that it isn't a case of you and mom against him. How" friendly" you are to him - being professional of course may help ease the situation. If it doesn't then there may be something else you need to address. Even what you have said so far has all been about you and the mom talking and really it has been behind his back as compared to the three of you so he may well feel that you are not on his side at all and if custody issues are coming up then he needs to know that you are neutral and care only about the best interests of the child.