@TheCoralBear ,
I'll start by acknowledging that I think it was ill advised of your husband to say go for it, and then when you got it, give an outright no, without explanation but maybe he didn't want to hold you back and now the reality has hit home, he just can't face it, that is only human.
But you aren't giving much information here except for your desire to go further your career in the USA and so it would be helpful if you could answer a few questions.
Has your family ever been to the States?
Just a thought but maybe your husband looked at working visa's in the USA and found issues that could be problematic i.e. he needs a job offer from a USA company to qualify, does your husband have a criminal record, or is he a member of any, shall we say, less popular groups or societies that may affect his right to enter the USA. Does anyone have any medical needs or special needs and if so how will you fund this in the states? Do you have significant savings that will fund this move, do you own your home or rent and if you own it, will you need to sell it to fund this as stuff like this could be financially difficult for your family?
How old are your kids? I wouldn't be looking to move if they were in high school as the different curriculum could compromise their achievements in the short term.
Also does DH have a career that would be affected by temporarily moving to NY because if I am honest this does not sound like a temporary move.
Finally and I understand why you may not want to explain this, but I also suspect that the fact your DH gave up his parental rights suggests there is another whole issue here that may affect the rationale for this move and you are really asking us to offer advice with a massive big part of the picture missing.