Or are you suggesting that Chris would just be a pain in the ass, even if he had no legal leg to stand on?
Both. By the rules of intestate succession it seems Cole Smithey is just as close a relative of Barb's as Chris is, and so they'd be entitled to half-shares, barring weirdness and assuming Barb inherited the entire property upon Bob's death, which is what would usually happen since married couples generally both own the entire property, which devolves on the surviving spouse.
I'm assuming Bob didn't do something odd like leave Barb a life estate to allow her to live in the property the rest of her life while somehow leaving the remainder ownership to Chris (I don't think that would have been legal anyway without her permission or somehow having excluded the house from the marital estate).
So I could easily see Barb having left the entire property to Chris in a will, as she would be entitled to. Clearly, he's the one who actually needs it. And Chris, whatever his flaws, has always been there for her.
I think the situation is probably pretty clear cut, though. Either Barb has clearly left the property to Chris, or to Chris and Cole either on purpose or by failing to get a will. In either case, one of them has no leg to stand on and it should be obvious which.
However, even with no leg to stand on, Chris has the advantage of actually occupying the house, so it would take something to get him out of there. The question is how much money he'd waste forestalling the inevitable in that case.