DaVe - I'm not sure your 2nd point is accurate. The OP stated that the husband/child do NOT have a visa for the US in their Argentine passports. So presumably they would in fact have to show their US passports at the airport (as proof of being able to enter the US) when leaving Arg even though they are exiting on Arg passports. (Every time I go to a country where visas are required, I have to show proof of having visa before boarding the plane to said country).
Again, they may be able to enter the US on an expired passport but I would be awfully hesitant to gamble on that being easily done.
But the bigger issue (for me) would be if the airline will even let them on the plane with an expired passport. According to a few posters here, they could not.
AGain, I will ask the OP - since it's 3 months away - why would you not go to the US Embassy in Buenos Aires and just get new passports instead of running the chance of getting denied entry?