We are going through same issues but from Canada to UK. Im from the UK and have now lived with my gf for nearly four years out here. I gave up a really good job basically and now i have got the chance to get it back as my gf wants to go to school in England.
There are lots and lots of issues that i wont go into here but best thing to do is to seek legal advise mate. With a lawyer they might be able to conclude it without going to court or through mediation.
Everything that is done must be done in the best interests of the child though and that doesn't necessarily mean they have to be kept in the US for that to be met.
What that means is the court will look at what is in their best interest. I.e if your gf had to split with you because you couldn't come to the US what would be the implications of that? A depressed mum wouldn't be in the best interests of the child. She would resent her ex even more and that would mean a very horrible situation that they would be in the middle of. Especially as the non custodian parent can up and leave whenever they want.
It would be against your gfs human rights to be denied to move. That then leaves the child. Is it in their best interest to remain with the mother or the father. If he hasn't played a very active role in their life then that puts your gf in a stronger position.
Even indirect stuff to do with yourself and your gf would effect the best interests of the child so its not just about them but about you guys as well.
How easy would it be for you to come to the US for example? Getting a work visa would probably prove difficult where as if she is already a stay at home mum looking after the child and you have a job she could get a fiancé visa or whatever and you could work in the UK and that would be in the best interests of the child as you could provide a home for them. If she isn't working and is taking care of the child it would be a big ask of the courts for you to switch roles. You would have trouble most likely getting a visa and she would then have to find a job that would support the whole family.
You would also need to demonstrate the strength of your relationship most probably in court. How long you have been together, your plans for the future etc.
If you offered access very similar what the child has now, im taking for example that its every second weekend then if you do need to go to court you can go in there demonstrating that you are trying to do what is not only right for you but also in the best interests of the child, i.e keeping access as high as possible and at the same providing them with a stable, loving home with two loving parents who can provide for them financially and give them everything they need to grow up to be a successful adult as well as still including the bio dad in that process if he chooses to be.
If the bio dad goes in there acting in a selfish manner, like my gfs ex will, only interested in his rights and what he gets he will most probably lose.
Its like a story i remember as a kid. The farmer and his wife bring their cow to the kings court and are arguing over who owns her. The King listens to each of their side of the story and then says ok i will cut the cow in half. The farmers face lights up and he says that sounds very fair. The farmers wife says actually no let him have the cow. I dont want any harm to come to her. The king gives the cow to the farmers wife? Why because she only has the cows best interests at heart thats how you want to come across in court.
Its a long drawn out process and the US court process may differ from here, although i dont think it will be that different.
The world is becoming a smaller and smaller place. Plane fares are fairly cheap now and with the internet and phone its very easy to keep contact. All them things should be in your favour.
Good luck
