I don't want to jump to conclusions because often in a forum it's not as cut and dry as it might appear. That said, I think it is somewhat presumptuous of him to assume you would pay his flight even though he'd stay with her. And as you phrased it, "then he informed us that he could only come home if we pay for the airfare because ...". Again, knowing that things don't always come across in a forum exactly right, it kinda sounds like he's giving you an ultimatum, 'pay the way AND let me stay with gf or I won't come home at all'... If it's as I am interpreting it, I'd carefully consider my next action. Out of the box thinking... maybe spend Thanksgiving in Colorado? It'd cost bunches more $$ but he's not controlling you that way. To me, the issue is not quite as much that he is staying with her while you pay, but rather the apparent attitude that is going with it, telling vs. asking. Realize that the gf (and son) want him to come home too. Calling his bluff is an option as well. Christmas is right around the corner - what happens then? Will this establish a precedent for future visits home as well?
Again, I know sometimes things don't come across exactly as intended on a forum so it is possible that I am way off base with his intent. If so, we're back to the other issues (monetary etc). By the way, is the gf in the same town as you? Is she living on her own or still with her folks?