I might be biased because I'm from NY and we raised three kids there for many years, although have done two international moves. I agree that the US is a complete shit show at the moment, but NYC really isn't. It's a fantastic place to live and have a family (especially teens) if, and this is a big if, you have money.
If you can afford a nice place to live in a nice neighbourhood, good health insurance, and, in your circumstances, send your DCs to the British International School, I suspect you would all have a fab time. I suspect, though, that with arts salaries being what they are, the above wouldn't apply and being a starving artist in a crappy apartment with 2 DCs is not the same as doing that in your twenties. I also think your husband will have a difficult time getting a work visa, and even if he can, it's likely to be slow.
I do think most kids that age are reluctant to give up the familiar, but on the flip side, it can be an absolutely fabulous experience. As a family, we wouldn't trade a moment - even the though ones - of our moves, and as a result, we and our DCs have friends all around the world