Your house, your rules.

I have had friends here with kids and if they're doing things that we don't let DD do, they get pulled up on it - if the parents don't do it, we do. i'm quite adept at saying "sorry buddy, that's not the way we do things here". Thankfully most of my friends have very similar parenting to us, and have no drama with me pulling their kids up (nor do i - if DD is doing something wrong, i expect her to be told). Children learn boundaries only by being shown those boundaries and being consistent in showing them.

if the parent doesn't agree, they have two choice - suck it up while the child is in your home, or ask someone else to look after the child

as for toys going home a simple "no, that has to stay here, you can play with it next time" - if they have a tantrum, too bad - again they need to learn there are limitations and not everything is theirs. "sorry, i know you want to take it home, but it's not yours, it has to stay here - you can play with it next time" (and i'll be honest, tantrums soooooooooo don't work for me, they make me more determined to gently teach the child about boundaries)