'I know that I am blocking his father from eventually wanting to see his son but in 4 months he made no emotional or financial connection with our son.'
You're comparing 4 months of this child's life against the next 18+ years?? Wow.
I understand that with the father being 'happily married' (which I seriously doubt if he's fooling around), it makes things that much more difficult....but what you need to understand is that this is about THE CHILD, not the father nor YOU.
Let me ask you some hypothetical questions:
You say he's happily married, which I doubt for the simple fact that he has a child outside of it. And there's NO way he will be able to keep it a secret forever...heck, Arnold Schwartzenegger couldn't even keep his secret. What happens if he gets divorced in the next few years? What if he wants to get involved 5 years from now? Ten years from now? You realize that the child is an American citizen, right? And that the US does NOT recognize dual citizenships, right? It is always possible that after you leave, the father could file a petition in family court for
paternity and custody....which could force you to come back to the US and resolve the issue, including staying here at minimum until the child is 18 years old.
You run an incredibly high risk of being in legal trouble if you were to leave the country. Stranger things have happened, but it's even remotely possible that if the father were to file and win a petition for paternity and custody, he would have the right to come to your country and just take the child. There have been a few high-profile cases in recent years where fathers have fought long and hard to get to their child who was taken outside the US and have accomplished it.
'Don't bl;ame me for not letting my son grow near his father....' Yes, I would blame you if you were to take the child out of the country...the child certainly cannot leave on his/her own. It really doesn't make any difference whether the father gets involved now, a year from now, or 10 years down the road. Unless you get it
legalized that the father is willing to give up ALL his rights to the child and legally allows you to leave the country, for the sake of the child, you need to stay here.
Think about it.....this child is innocent. You and the father have put this child in this position and, as the parents, now you have to do what's right by that child, even if that means doing what you DON'T want to do.