Daycare children can never be left unsupervised for a minute, so it should not be hard to observe this child and see how he acts.
I would say just stop talking about it at this point unless the behavior contiunes. Try and make sure that they are never left unsupervised for a period of time (I know harded to do than said). Also maybe have a group meeting with all the kids and go over your DayCare rules again--about personal space and what is acceptable behavior. This way it is not going to single out any one child but they will all get the same message at the same time. I would say after this meeting if the behavior continues you can then tell the mother about her sons behavior and then you can decide whether or not you want him to be part of your home daycare.
I spoke to my daughter and the other children seperately and they all say that what he said is untrue and that he kept jumping on there backs when they were playing kittens and dogs and as my oldest stated humping them. My oldest daughter and the other two had the exact same stories. What do I do? Obviously he is lying and now how do I tell his mom? We are on good terms but all mom's hate to be told there children are lying. And why would he make up the story? I am thinking for attention but who knows.
How old are the children? This sort of behavior does not spontaneously occur with young children. It occurs when they have been exposed, either directly or via some other stimulus (movie, pictures, e.g.), to such behavior, and then they imitate it. Without having to investigate re: the veracity of any of the accounts, trust what your eyes observed. It would be sensible to speak with your own children in more detail about how the behavior came about, while continuing your attempts to teach them that such behavior is not permitted. If you and the other children's mother are on good terms, you might consider a discussion as a group to underscore the uniformity of expectations.