We have taken her to Mexico before. They didn't look twice ate her when we came back across the border.
Of course, if we went to the consulate and told them our story, they might clue in and suddenly decide that she can't come back.
It's going to be expensive, but at this point with all the decisions already made by the agency, I don't see any alternative. They are going to be even more reluctant to undo what they have done and confess that they were wrong. They will probably have to be forced into it, either by a lawsuit or by serious influence from a senator or congressman.
You also need to make a total pest of yourself in your congressman's office. Just sending one letter is not going to get their attention - they get hundreds. (Don't contact the media until you have exhausted that avenue.)