The rules say you can move the kids out any time after they become Young Adults. Teens must have an A in high school before you age them up to Young Adult. They must also have at least one character value in range for earning a trait if you have the Parenthood game pack.
Mods that give an unfair advantage over other players are not allowed. This specifically includes mods that increase household size.
I based my answer on the rules found at these two locations.
https://snarky-sims-witch.tumblr.com/post/181535303038/the-sims-4-100-baby-challenge
https://docs.google.com/document/d/1z7DJgxbyViBnE93PEnBHk6iGSjbWOfoit9xiYPMNM6Q/edit