Hey there,
I thought I would give an update for anybody in the future reading this thread. I landed in Santiago for a week. The gate attendant in Atlanta didn't ask for anything besides our tickets and passports. The passport control didn't ask for exit tickets (although we had them already). He just wanted birth certificates for the kids.
From Santiago to BsAs, gate attendant didn't ask for anything and passport control didn't even ask for birth certificates. I did ask him a little about boarder crossings and he said what I expected, they don't care much about visa runs until the time in country adds up to about 6 months, but he was super relaxed and very friendly.
We still don't have an exit plan for Argentina and nobody cared, but thanks to this forum I had a plan to quickly buy a ticket if it came to that. So for that I'm thankful.
Although I appreciate the forums, I think I read them too much and get over worried about every possible problem. Just my nature I guess.
Next week I think we look into getting our visas before our FBI background check time elapses.
Thanks again everyone.