We know this behaviour from dck is common. When one of my dck starts these antics, I will have a chat with them just before pick up to remind them how they are expected to behave and I say this in a stern voice with eye contact. This always helps though if they start the misbehaviour then I give them the stern eye contact as a reminder of our chat. I also when I can, have them partially dressed for the trip home.
As for Mom, I would hand her dck's coat and tell him mommy will put this on and then back off and let her deal with him while I attend to the other kids or just tidy up. Message clear - he is your problem now.