I'm a parent, and I think it'd be overkill to say "Don, I never want your partners around my kids at all". I do think it's reasonable to say "hey, I'd like to meet partner before they join you & kids on an outing".

And that said, thinking about it from Alan's side -- if I'm seeing someone for casual sex, I wouldn't *want* to go on an outing with them and their niblings; I'd say "sorry you're busy that day; wanna come by after you take the kids home/try again in a few days?" But if after three months I'm wanting to keep the person around and see where things go, I'd be up for it.