Chris is the next of kin, followed by Cole, followed by David and Carol. Since Bob died first, Chris and Cole have the strongest claim to the inheritance, with Chris taking priority. If Barb dies with a will giving it all to Chris, then Cole is out of the picture.
If Barb is no longer there, Chris can certainly move back to the house with Barb's permission, but payments on the mortgage must continue. If Barb dies, Chris is free to inherit the house as long as he continues mortgage payments, which could be low enough that his tugboat could cover them, however Barb's other creditors, at least previously, had ~20k in debt that Chris would also be responsible for if he inherited the house. He would also have to make good on those payments to keep the house.
If Chris could secure a HCV, combined with his tugboat it could make mortgage payments and pay off the remaining debts on Barb's estate. Also, it looks like the homestead exemption in Virginia is now $25,000, so if they managed to get their outstanding mortgage debt to under $25k (VERY doubtful has they had closer to $75k last I heard), Barb's estate could declare bankruptcy and discharge all of her other debts, leaving Chris only responsible for the mortgage.
Of course all of this would require financial management that Chris does not possess, so someone else would have to set him up with it, and he would also have to not fuck it up. Realistically unless someone is seriously managing Chris, he will no longer be able to live at 14BC.
EDIT: Of course if Barb sells the house at Aunt Harriet's instruction, or if Aunt Harriet gets power of attorney, then Chris' wishes are completely null and void.