We have no idea about a pre-nup. I have reason to doubt that they did.
Community property doesn't mean what you say it means in your state, in Arizona or California or Nevada. Community property law in general is described here:
Community property - Wikipedia
(First paragraph).
No, it means that the kitchen becomes community property, as it is part of the house. If you bought a car with your inheritance and put the car only in your name and no one else's, it would stay separate.
Whatever you take out of your inheritance fund (home equity, cash) and spend on a jointly owned project (house) becomes commingled and is no longer your separate property. It becomes like everything else you earned during the marriage.
In this case, if the funds were already commingled (and I bet they were), then RT is now the only owner with access and will remain so. If he ever manages to marry again, he might want a pre-nup to protect those assets if he didn't spend it all down in the meantime. If Barbara doesn't show up, he'll need to go through a lengthy process of having her declared dead (5 year wait) before he can remarry.
If they were not commingled and she had a separate account for them, and she did not have a will (she probably did but who knows? who would know where it is except RT? no evidence they had a family attorney but we just don't know) then he has to have her declared dead. He will inherit the funds unless a properly executed will is found that distribute the funds to someone else.
Right now, all their joint assets (house, probably truck and trailer, maybe airplane) are in his control. If she doesn't show up, he can write a will and dispense these items to whomever he likes upon his own death. Not sure what happens if, 10 years from now, Barbara has not been declared dead. I think RT's heirs will likely have to go through that process to probate his will.