Legal Question in Real Estate Law in California

No, not unless they are on title as co-owners. Being missing a short time (now just over a month) does not carry a presumption of death or trigger any rights resembling inheritance. There is a statute covering presumption of death after five years that the kids might want to review. It's Probate Code section 12401. The Probate Code also has general provisions for establishing and reporting the fact of death in sections 200 to about 234.

I'd assume unless there are other facts not given that if the childhood sweetheart came peaceably into possession of the father's property she has a right to continued possession and the kids have, currently at least, no say in the matter. She is, after all, a surviving spouse and even if they hadn't married, current possession must be shown unlawful by a claimant with standing to object, such as a superior right to possession, which the kids simply don't have.

Of course, proof of fraud or foul play could change the situation drastically.

A married spouse would generally be entitled to at least part of the estate upon death of the other spouse, and generally entitled to possession of the property unless other factors enter into it. There is no easy answer to your situation, but if you fear any kind of fraud or foul play, do no hesitate to investigate or report it to authorities. If so, you should consider hiring counsel to guide and represent you to avoid creating 'slander' type problems and claims. If serious about doing so, feel free to contact me.