I play the sims 4, but even in the 3 I had the technique to prevent them from moving out, it was to turn every maried couple into a playable household. So, for example, the son maries someone and goes out of the family. I would play with that new couple, making sure they have children and building a nice house. Then I would go back to the parents to go and marry off the daughter, and play with her for a while. Once all the kids of the first parents are married, setteled and with kids, I play again with the first son, making his children grow up and marry them off, playing a little bit until they all have a house and family. Then I would go back to the first daughter's house, do the same, etc...
Since each household had changed into a playable one, they can't make them move out