You seem to be assuming that Callista Gingrich is unrepentant of her past sins and thinks adultery is fine and dandy. That is an assumption, as no one can read her heart. She is certainly NOT marching in pro-adultery parades, or otherwise openly and publicly supporting adultery.
How do you know she hasn’t undergone penance? Just because she didn’t get scourged in public? So if you committed sexual sin with a public figure, you have to undergo public penance? Even though if she’d cheated with a married Joe Schmoe, and he later divorced his wife, got an annulment, and married her, she would not be obligated to do such a thing.
Anyway, Mrs. Gingrich may or may not be “qualified” in the strict sense, but it seems par for the course that most of the ambassador positions are sinecures, or close to it.
I doubt the Vatican would reject her based on being “unqualified”, nor do I think they would reject her based on her past sins. She is currently in a valid Catholic marriage.