I can tell you for fact as my wife came to the UK with a Vietnamese license. She was allowed to drive in the UK for one year from the day she arrived.
Insurance was no bother, and I bought her a fiesta ST for her first car, had a tracker on it for the first year but not this year. She had only got her license in VN a month before she came to the UK.
I taught her to drive, in her car on her fully comprehensively insured car. Not at all against the law, after all, all I did was sit next to her and tell her what to do.
She passed her test in VN on a manual car, so there was no issue with only being able to drive an automatic. If your wife has an automatic license only, then that is all she can drive one of those here too, if she has a manual gearbox license, then even if she has forgotten how to change gear, she can drive one in the UK. You can teach her.
Before her US license year expires, she will need to apply for a UK provisional, and do the theory and practical so she can receive a full UK license. She can still drive on her US license without worry, while she is preparing for her UK test and has a provisional. Best to apply for UK provisional and do this asap, because if she fails the UK license, but still has her US one, she can still drive herself and you can still teach her, she can then retake her test.
MY OH passed the theory first time, and then failed the first time for practical, passed second time a few weeks later, and no need to stop driving herself.