I've been down this road. Albeit as an Australian with a NZ ATPL and an American wife.
The right to work in the U.S. is crucial. Without it you are a tourist. If there is any way for your wife to leverage your right to work as a condition of her job offer then exploit it.
In the U.S, Part 121 (Airline) Turbine command time is king. Without this qualification your options may be somewhat limited to regional airlines with poor T&C's. If you have Turbine command time and a work authorization your options expand. Your competition expands proportionally as well.
Adding your 737 Type rating and your US ATP will increase your chances considerably. The two qualifications can be combined in one 'check ride'.
The administrative conversion of licenses is relatively easy. It requires paperwork, studying the published questions and answers, followed by a rudimentary flight test. Getting a job is highly competitive as always.
Best wishes.
