So what I am hearing as the general consensus is: exit US with US passport, enter Argentina and leave Argentina with Argentine passport, and re-enter US with US passport. Does the US not care that you have no stamp in your US passport when you come back?
Airline tickets are booked in US married name consistent with US passport. I have read on the airline site that as long as your US passport says Argentina as place of birth the airline won't hassle you for the fee, but she can bring her Argentine passport in case. I guess the one complication is that the Argentine passport is in maiden name and US passport is in US married name.
I suppose the simplest way would be to plan to stay for less than 90 days and just use the US passport the entire time for all international travel and border crossing.