Plaindriver:
You'll need a Greencard to work, basically. I presume your wife is being sponsored for one, probably because a Company has gone in to bat for her with the INS? If so, as a permanent resident, I believe she will be able to sponsor you as well, though it takes time (could you consider commuting to the US in the meantime? NYC is easy to get to from UK...perhaps not so from my and your hometown, Edinburgh). The INS website is awful but has a flow-chart somewhere on it for you to follow, last time I looked.
As regards to licences: you go to the FSDO for the FAA, and they review your quals. You need them to auth. you for doing an abbreviated course of ATP writtens and Flight Test. Many schools in FL specializing in this, and it actually makes for a relaxing mini-vacation (the Flt test is thorough, though - don't get me wrong).
As to jobs: no idea how much time you have on the 737, etc, but the jobs are starting to open up here with some of the more desirable carriers if you have high time. FedEx, UPS, CAL, AirTran, Virgin USA, United are all accepting resumes, I believe. The commuters here are a grind...probably not your cup of tea, even if you've been flying for Easy or Ryan. My airline, AA, has 2000 still on furlough, but we're moving through the list and about 1/2 are not coming back - gone elsewhere. I just did a very comprehensive review of where we stand IRO other carriers around the world (I've flown for 6 others), and we still compare v. favourably in some areas (particularly: travel, commuting, schedule flexibility and pension) and not so good in others - pay (collapse of the dollar), medical costs, stagnation.
Finally, you might want to consider CX freighters based in NY...but I'm sure you've heard all about the in's and out of that...
PM me...I'm getting old, and some of the above may be out of date; hopefully others will correct me here where I am in error.