OP - if your child lives in the US, he won't see the UK as his home any more. That's obvious, surely?
I am British, married to an American man, live in the US and my children were born here. It is a source of sadness that my children are American, mostly because that makes them different from me (I don't think much of either country, truth be told). BUT, that's all my fault for marrying an American man. They're literally half him, and he's American.
Your children will be fine, as long as they're in a stable home ideally with both parents. Where that home is doesn't matter so much as the home environment. I will say that personally, I think most of Florida is the armpit of the USA and hell would freeze over before I lived there - hence why I'd never have married a man from there or any of the other places in the world I'd never want to visit or live in. Unfortunately for you, that ship has sailed. You've had a baby with a Floridian.
Personally, I would focus on your own mindset. There is a HUGE cultural difference between anywhere in the UK and anywhere in Florida. Huge. You need to decide for yourself where you want to live and take it from there. Your child won't be happy if you're miserable.
I can't believe this has never come up before, that only now is it a make or break thing. Did you really not discuss this stuff before you got married? Before you had a baby? Have you ever been to Florida? Which part is he from/would you move to?