Let me start here - You have a green card, so you won’t have “any” problems finding a job. I said “any” cause obviously that’s still very relative. But from USCIS point of view you’re not a foreigner per say. You’re a permanent resident, so you’re just fine. We have many green card holders at US airlines.
I disagree EK will give you QOL over regionals. You see the obvious - tax free salary, housing and etc. But have you wondered about your rest, flight hours and etc? Flying for any middle eastern airline is exhausting. Also look at QOL in long term perspective. Completely different benefits and you can only live in the UAE while you’re employed. And what about your wife? And possible future children.
You say starting pay at regionals isn’t a lot, but your wife seem to be highly educated, so look at it as an investment. It will pay off. Way more flexibility. UNIONS (if you care for it). Labor laws....