I did a spell working for Costain in a HO role so know something about the UK side of things and of course the US.
Sounds like you are talking about an EB3, now that takes a few years and costs the employer a bunch so you have to know someone, really be top of the game for any company to consider this.
Maybe your wife could look at an E2 to open a Hairdressing business, now an E2 is not Permanent Residence but can be renewed indefinitely.