I stay b/c most of the time I don't know the parents that well. I just tell DD where I am sitting JIC she needs me but most of the time she is happily playing and participating in the party.

I'd ask if the other kids can come & say that you are happy to pick up the tab for them. I had a lady ask if her son could tag along & I had no issue with it & was happy to pay for him too, but some people might not want the added expense. If they aren't going to be involved in the party then I'd not bother about telling the host they are going to be with you.