So, let us know how you come out.
Suggestion:
1) Thnank the dealer for getting you in right away (they didn't have to, but they did. And that was nice of them)
2) Ask the Dealer to contact GM about the mechanical breakdown, and ask them to ask GM what GM can do for you (again, not this dealer's fault GM built a bad engine; but by being nice to them, they may be more apt to assist).
3) If the dealer cannot get you square w/ GM, then ask for the GM reginonal service rep's number and give her/him a call. If she/he cannot be reached, call GM roadside or GM Customer service, and convey your story (nicely) and ask for what you would like GM to do: a) get vehicle fixed at this dealer --they are obligated to do this, b) Arrange for a rental or promise to reimburse a rental so you can get your family home, c) ask about the "vehicle reunification program" which I think is what GM has when you have a breakdown tha takes time to fix and you are far from home...I believe they ship it back for you, or fly you baack to get it