Off the top of my head, maybe there already was a Dwarven King of the Blue Mountains when Thorin came there. I mean, do we know what happened to the Dwarves of Belegost and Nogrod (the Firebeards and Broadbeams, IIRC) after the drowning of Beleriand? Did they all migrate eastward and merge with the Longbeards of Khazad-dűm, or was there a Dwarven community of some size left in Third Age Ered Luin? If the latter, I guess they would have had a king of their own - who would certainly have harboured and honoured Thorin, but would have been wary of any attempt to usurp his throne or set up another kingdom in the neighborhood.
To answer your more general question, I think the Dwarves, even if forced by necessity to set up new dwellings if driven out of their old ones, didn't forget their former homes so easily. They never gave up the dream of retaking Khazad-dűm, as Thrór's and Balin's stories show; and as long as this wasn't possible, Erebor seems to have been the thing coming closest to Home for them. Or maybe they were just fed up with being pushed around across the map. On the meta-level, we know Tolkien modelled his Dwarves in TH and LotR on the Jews to some degree, and there's something very Jewish in this longing of a wandering people for the Promised Land - Dwarven zionism, if you like.
(x-ed with Zil)
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Und aus dem Erebos kamen viele seelen herauf der abgeschiedenen toten.- Homer, Odyssey, Canto XI
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