The issue with each of them taking half and renting is that dad could blow through his half, and then what? That solution seems to have the same potential for disaster as selling the house and having dad hold on to half while they shop for a new place to buy. If he can't be trusted not to blow the money in that scenario, he can't be trusted not to blow it in the rent scenario. (In fact, the rent scenario is probably worse because he has to not-spend the money for a longer time.) I know you said invested "in a way they can't touch the money", but just make sure that's iron-clad.
And also consider what happens if dad blows his 4% disbursements on hookers and blow and then mom is in a bind when it comes to paying property taxes (or rent), utilities, maintenance, etc. If you go this route, you might want to have much of their 4% allotment sent to some sort of untouchable account (perhaps directly to you) so you can pay the necessities, if you are up for being that hands on. Dad can't blow the property tax money and the roof replacement sinking fund and the money for electricity if it goes directly to you. But you may also not want to be that hands-on, and deal with the almost inevitable whining and frustration that will happen when you are mean and won't give someone what they want.
If they decide to dissolve the marriage, what happens to the split funds? It might be worth consulting an attorney about this. Mom's inheritance might be okay (depending on your state's rules) since it sounds like she will keep that completely separate. She just needs to ensure she doesn't accidentally co-mingle funds, so the best bet would be that the account stays as the inheritance and only the inheritance, with no future deposits. But if they sell the house and each take half and dad blows his, mom's account may still be community property, so dad could be entitled to half of her half when his half is gone.