First off, I do not advocate sleepovers for adults until the relationship is “serious”. Little kids can become too attracted too fast and if it doesn’t work out, there is the whole separation thing. To older kids, it might send an ambiguous message, especially as they grow into their teens. Besides, no kid ever wants to conjure the picture of their parent intimate with another person–ever!
But, if you are in a relationship that is indeed serious, one of the easiest and most non-issue generating ways to break the ice is a vacation. It is even easier (believe it or not) if the other person has children as well.
Two room, or two cabins are booked and it is as simple as grown ups in this room and kids in this room. Usually, the kids do not even notice and it is a cool time to be alone with other kids.
Now of course there needs to be caution with mixed gender teens! Maybe three rooms are the solution–grown ups, boys, and girls!