I finally decided I'd rather start a new generation rather than let the two kids still at home starve. Just in case they don't inherit their parents money I spent it on the house and food, and both were intact when the kid took over.

That's good to know!
The following may be a possible spoiler, so I'm listing it as such. Read it if you feel you want to know what happens to the kids when the you start a new generation.
The game made all the kids, even the two that were underage, old enough to take over the house. That was such a relief, as I pictured them being put out on the street. The youngest was 12 when the last parent died, and is 23 now. I chose him, since I think the younger they start out the more chance they'll have to succeed.
I still don't know what would happen to a remaining parent when you change generations. Though I feel much better about the outcome of the remaining kids.