Your original post indicate that you get together often with this family outside of daycare. One issue may be that the child is confused in the sense of if he does something bad outside of care you do nothing which of course should be the parents reacting. One one of your outings if child misbehaves speak to him yourself with the idea of saying I don't care whether you are at your house or my house or the park we do not hit our friends. Then put your hand firmly on his shoulder and make him stand with you or take him to sit in a lawn chair beside you. Do not engage with him but just sit there. If he gets up put him back in his chair. Remind him we have to sit out if we don't play nice. Then after awhile get up and take child with you back to the action. Let parents know what is going to happen. If they see it they need to do the same. Sometimes a child is testing to make sure the parents and daycare provider are on the same page.