So they leave the house around 18+?
If this is not a spoiler further to the title of the thread, who lives in the house after the last kid leaves? Just their parents? And if so, how old can the Mother have children to?
The house and all of its repairs and upgrades passes to the next generation. When the house can be passed, the family screen will have a button at the top. You can choose which child to inherit, and start a family with them.