It is not impossible for state schools, but it is rare. The following article talks about some who came to New Mexico. Most of these came on J-1 visas - not a great idea as you can read in the text. You would most likely want an H-1B. A key thing to note from this article is that NM schools are hiring mostly from the Philippines and India because NM salaries look good to them. They would not look good to you. Not mentioned in the article is that NM also hires a small number from Spain, largely because of the historical cultural connections. Good luck.

https://www.abqjournal.com/1233198/f...y-nm-jobs.html

I came via an L1a, so can’t help on the teacher front. Probably not viable on a teachers salary, but if you are independently wealthy for $900k-$1.8m plus some lawyers fees you can effectively buy a green card and that will let you work in most non government jobs.

I would contact the State of Alaska. They have many schools in remote areas that serve the native population. I am thinking some positions may be hard to fill but salary should be good and it would get your foot in the door and provide a source of references for work in other states.

Yeah, worse than I had thought. The ongoing fees and percentages are unjustifiable.

So, for the OP, short of getting directly sponsored for a green card off the bat, it’s going to be very hard to find an ideal situation that both gets her here and allows her partner to work.

Teacher salaries are highly variable around the country, but can IMO be generalized as not very good. I assume that the private schools would be somewhat better?

I’ve heard that private schools pay worse also!
Teaching salaries vary widely from state to state, as do the number of vacancies.
I’m a qualified, experienced UK teacher who moved here on a spouse visa with my husband, now has a GC and I’m in the process of getting certified in my state. It costs money to do prep courses, then more money to take the exams and get my qualifications evaluated. And if I then get my license I’ll have to do a masters within 5 years or otherwise I won’t be able to renew my license! It costs a lot!
On top of this, in my state, jobs are few and far between as people literally stay in the same job from graduation to retirement!
I couldn’t imagine many places paying thousands of $$ to get a visa for someone from the UK. As a pp stated, maybe only in a very rural area/state that struggles to get applicants, and even then it probably wouldn’t be a visa with an easy path to a GC, or even somewhere you’d want to live!