Laurakaycraig~
Let me try to offer up an explanation that you can understand.
Parents have one window of opportunity to prove that they are a more fit parent than the other parent in a divorce proceeding. That time is at the time of divorce. If one parent fails to prove this, or simply does not show up, then they have lost that opportunity.
From that point on, if the noncustodial parent (even in the case of joint custody) wishes to have custody changed so that they gain primary physical placement, they must show a change in circumstance which affects the welfare of the child. This is not simply proof that the parent doesn't do dishes often enough or talks on the phone too much. That is not enough. Generally, you have to show severe neglect or abuse for such to even be considered. You cannot show such, therefore, you will not get a change in custody. Furthermore, you do not even live in the same state, much less the same country, so a judge will not even consider it.
Now, I know that you said you made mistakes and you regret them and if you could go back you would change it all, and so on and so forth...
Let me ask you this, how many noncustodial parents do you think change for the better?
How many noncustodial parents wish they could be there to tuck their children in at night, help them with their schoolwork and be available for all their needs?
How many noncustodial parents think they are a better parent than the custodial parent?
Probably most. The point is, just because you realized you made a mistake, doesn't mean the courts are going to change anything. We all make mistakes, and sometimes we have regrets, but most of the time, we still have to pay for those mistakes.
Heck, sometimes we pay for mistakes we didn't even make (just imagine being the noncustodial parent when you didn't even do anything wrong! It happens all the time.)
My dh never even had a chance at being the custodial parent, because bm automatically got it by default.
The point is, the mistakes you have made, whether you are sorry or not, have cost you primary placement. There is nothing you can do about this, except to move back home so that you can see them more often. The fact that you STILL live in the UK indicates to most people here that your children are not your first concern. You should have put your new love on hold, because while you may be sorry for the mistakes you made, you still haven't changed. You're STILL in the UK!!!
If your husband loves you, then he will move to the US so that you can be with your children. It's that simple.