I have the latest patch, which it says is supposed to have a "move out children" feature or something but how do I use it? My Bard and my Knight (not married, I don't want them to be married) have five kids together, and obviously I have no room for them all in the tavern so I want to send them to live with their father (they should live with him anyway since kids of two Heroes always follow their father's profession, so all of them are knight apprentices).

This cannot be done. If you decide to have another child, then you may be able to send a kid to a nunnery.

If you get the parents married and then get them divorced it should ask which household you want the kids to live in. I know this happens for kids born in wedlock, I assume it'll be the same for this case since he's the father