Usually when a husband leaves they are fed up about something or don't feel appreciated enough to stay. People don't usually know anything is wrong with the marriage until one partner leaves and then they realize that things were bad but often times they feel it's too late then but it isn't. Time is what your husband needs right now but before you give him time you need to sit down and think about all the ways you may have taken him for granted and criticized him, then write a letter make it as long as you need it to be, in the letter apologize for everything you took him for granted and for each one you come up with explain how you took him for granted. If you just apologize and don't know why you're doing it then it won't mean anything he will take it as you just apologizing because you don't want your marriage to end. There is a reason that things have made it to this point, and it is obvious that he needs a break. Allowing time for reflection and thought is the best way to evaluate your relationship. This also gives your husband time to clear his head and calm down. It could be that some time away will remind him of how valuable your relationship was. Absence makes the heart grow fonder; he may realize how much he misses the two of you and change his mind about staying away.
In a marriage it is very easy to put the needs of child(ren) first and often the husband is left feeling alone and unwanted or needed. This is natural when you have kids, but it also means that you may have lost some of your attention for your husband. Your husband didn't fall in love with the maid or the mommy; he fell in love with you. Reconnect with who you are and what makes you happy before you try to win him back. After writing the letter to your husband cut off any forms of contact with him for at least two weeks. That means no phone calls, text messages, and letters or seeing him unless he wants to talk to his child or come see his child then you make it only about the child. Don't beg him to come back that will only make him feel like you are respecting the time he needs to think things through. You need to go out and start to rebuild your confidence. Whatever you used to do for fun before you were with your ex is what you need to be doing now. Go and hang out at some friends houses, go to a few diners with friends, find a hobby that you like to do what ever you need to do to get back your confidence, this will help you realize that you had a life before marriage and your daughter. You have to find you again in order to give your husband the attention he needs if he comes back to you. After the two weeks ask him if the two of you can talk about what has happened for the sake of your daughter. By this time he will have gotten the letter and had time to think about the content in the letter.
You are going to have to find a way to apologize to him in detail and acknowledge that you understand now what it was that was part of the reason for him leaving, if he doesn't think that you are being sincere it will only make him want this separation and possibly a divorce even more. The way you communication your feelings during this time is very crucial to helping to getting your marriage back on track. If he doesn't speak English very well how did you communicate to him?
People say things out of anger and then realize the things they said they said to hurt their mate that is why it's crucial to give him a cooling off period. It is when both parties give up hope that the relationship is over. I would still give him a couple of weeks and then talk to him if you have a way of contacting him. If in that time he still wants to end the marriage then you may have to consider beginning to find closure in your marriage. He could either feel one of two ways "Absences makes the heart grow founder" or "Out of sight out of mind" let's hope in that time he will feel the first. You can best believe even overseas he will be thinking about you and his daughter and the situation at hand. It's not that easy to walk away from a marriage like that.