I don't envy your situation. I agree with what most have said here, that a man who really loves you wouldn't ask you to make such a huge sacrifice when he's done virtually nothing to help you transition over to Manchester.
I guess part of my confusion is, if your ex-husband is such a controlling person, why did you leave your daughter in his primary custody? You've said previously that until recently, you didn't have much contact with your daughter. I think it's great that you want a solid relationship with your child and honestly, any man who would force you to choose him over your child is not worth having.
Men come and go. Your daughter has one mother. You.
It also appears that Katrina is going from one controlling man to another (with help from the latter's Mummy). I don't know how the ex-husband controlled Katrina, but it sure looks like the new male (he is less than a man in my eyes) is calling the bulk of the shots here--when Mummy isn't.
Katrina, why would you want to go from your ex controlling your life to another male and his Mummy controlling your life? I'm seeing a pattern here, and it can be broken. Love is not control. It sounds like your current male's life is much more about him and Mummy (who seems to have a lot of control over him) than it is about you. If guys like this are a habit in your life, it's time to break that habit.
If you want to have a good life away from your ex-husband, you can have one 1-2 hours away and still have a more easily-maintained relationship with your daughter. It would be a lot easier to drive 1-2 hours to see her than it will be to fly internationally.
If your heart is in the UK, so be it, but please think long and hard before you put yourself into a situation that may be no better than what you're leaving. You could give up everything in the US only to find that the UK is a case of "same s***, different bucket." Once again, I wish you luck, peace and wisdom. All the best with whatever decision you make.