I would try to divide behaviour into:
a) things I have to deal with because they affect other people/property right now
b) things I can ignore because it is not my job to see that this child grows up into a civilised human being or even survives beyond the end of this playdate
In the second category I would place fussiness about food, sulky expressions, refusal to take part in things, refusal to tidy up etc. Not my job; I would pretend not to notice.
In the first category I'd place fooling around with keys, fighting, throwing things, anything resembling bullying. Firm but brisk "don't use the key again" would cover it for the first instance, repeated ignoring would result in threat of sending home.
I would also try to have most of a party (as opposed to playdate) organised with something like a treasure hunt, other games, food and a definite finish time.
Actually, what I used to do at parties was to skulk in the kitchen (I am Mother, right? I have an Important Job doing the catering) and let dh lead the games.