Quote Quoting going crazy
1) As the Father what legal rights do I have with my USC son. Do they extend here to South America?
Tread carefully. It is possible that the U.S. would enforce a custody order from the nation in which you reside, and given your residency in that nation it is quite possible that the courts there would issue a custody order to your wife if she filed for custody after you left with the child. Meanwhile, you would have to meet the jurisdictional requirements of whatever U.S. jurisdiction you move to before you could file for divorce and custody. Check also with a family lawyer to see if the nation in which you reside is a member of the Hague Convention on the Civil Aspects of International Child Abduction.

Quote Quoting going crazy
2) Should I help my wife finish her papers or does that give her more rights against me?
It would probably simplify parenting time issues (and diminish travel costs) considerably if she were able to live and work (if she so chose) in the United States. What will you do if she gets a custody order making her the primary custodian, yet she has no legal right to live and work in the U.S.?

Quote Quoting going crazy
3) What options (or suggestions) do you think I have?
Work with a good child custody lawyer, starting now.