My sim couple have two children. When the children reach adulthood I want to move at least one of the children out of the family home into their own house, but ideally I would like to move both of them out.
So here's the question: If I move both children out and the parents die, will the game allow me to continue playing with one of the children's households? If it will allow me to, will the new household inherit the parents' home?

When the parents die (your ACTIVE family), the game will ask you to choose a new household to play, at which point you can choose whichever INACTIVE child's household you want to continue playing with. The children, however, will not inherit the family home, although now being vacant, I guess you could just buy it and move them back.

NRaas StoryProgression together with its SP Money module has settings that govern inheritances a bit better than EA has arranged. You can also designate a home as Ancestral so it stays within the family when the last member of its household dies, even if these aren't the sims you are playing.

But for your purposes, and just to be sure, wouldn't it be simpler to move one of the children back in around the time that the last elder to do so in the parents' house reaches the end of their life expectancy?

Thanks guys, that's very helpful. I didn't realise it would ask you to choose another household. I use NRaas StoryProgression some of the time so I'll do as you suggest and make the home ancestral.