Even if your husband initially agreed to consider a move to New York, but has now changed his mind - you can't force him to move. Yes, I completely understand you're upset and frustrated, who wouldn't be.
If your husband doesn't have parental responsibility for the children, then yes you could force the children to come with you. However, it would be the end of your marriage and you'd have two very unhappy, distraught children on your hands, who would be unlikely to forgive you.
You need to look into the ability for your husband to be able to work. How easy would that be?? New York is very expensive city to live in, not just in rental prices but the cost of living too. What are the schools like? How easy would it be for your children to integrate? Your daughter is 14, so she's likely Year 9/10 at school, so she's getting towards her crucial years education wise. If you had to come back to the UK from the US, how easy would it be for her to slot back into school with GCSES??? I think that could be tough for her.
Personally, if you want to go (and it's an amazing opportunity), you need to go solo for at least 6 months. There's no point in uprooting the entire family, if the production closes down within 6 months. You have no way of knowing if this is likely or not. I appreciate you don't want to leave your family behind, but the reality is, you can't have it all ways. Your husband and children don't want to move to the US, and you can't force them.