Not having kids yet I haven't had to deal with handling behaviour during playdates etc, but I have dealt with behaviour management while working in childcare and OSHC. I will have to deal with this stuff a bit later though as we want to do respite foster care eventually and sometimes you will have to control behaviour, and it may be quite hard behaviour to manage given what the poor kids have been through (which you often don't know what happened, but it's bad enough that they ended up in foster care at least). It's more controlling the situation so neither the child nor anyone else gets hurt etc than discipline as such. They have pretty strict rules on what you can and can't do I believe anyway. It's just a pity you might sometimes get it wrong because you don't know the kid's history, so what you think is a simple and fair punishment is a trigger for them and is traumatic for them and makes them upset and also makes them behave a lot worse. I remember reading about someone who fostered and then adopted a child whom many had given up on and they found the child to be behaved okay for their age at first but then they gave them a time out and told to sit on a chair and that's when they first experienced the behaviour that turned most people off. When they adopted the child they found out what the kid had been through, and part of what they had been through was being tied to chairs for hours on end. That's not the most saddening story I've come across either - but it does show how you can use the wrong discipline techniques when fostering without even knowing because you don't know the kid's experience.
As for how you spoke about physical discipline, I don't agree with smacking etc anyway and I think it is ineffective but that is definitely off the table with foster care, both due to rules but also you'd like to think it's common sense not to hit someone who has been neglected or abused or whatever the case may be. Smacking is pretty ineffective anyway so that's no big loss. I don't intend to smack my own kids let alone foster kids.
Your post is interesting for the unique situation of play dates. It must be a hard one for people to navigate at times and I would imagine there isn't that much information out there about how to deal with discipline during playdates.