I believe that at least one parent has to die before you get the option. Don't worry...they die way too young in this game.

I have a family where both Dad and Mom have died, and there are still two kids at home. They're both deeply depressed and will probably starve if I don't start a new generation. I hate moving kids out of the house to do this though. I wish the creators had made it so that the new generation character would take care of the aging parent or siblings than remain. It's too hard to make them move out so the older sibling to take over.