First, you need to confirm that you too will be able to get a right to work visa in the US. That will probably be one of the hardest hurdles to overcome.
Then, you must get an FAA ATP for the B737. Rather than suppositions, contact flight training facilities directly. While I do not endorse any of these facilities, you can start with the following:
PAN AM International Flight Training Academy
Higher Power Aviation.
Then the last hurdle... getting a job. About the only us carrier that you would have a chance with may be Vision Airlines, a B737 operator. Miami Air International is another carrier, but given the fact that you would be in the US on a work visa, you would not qualify for certain clearances required for Miami Air flights.
Copa Airlines, a Panamanian airline is actively recruiting DECs on their NGs. Perhaps your JAA Certificate would be acceptable to their operation.
But first and foremost, you need to personally contact your wife's company and her immegration attorney for complete details.
Good luck with your quest, and I hope all works for you. By the way enjoy the Carnegie Deli... the best corned beef on rye on the planet
.