Just my 2 cents, but you need to get legal advice ASAP! She is leaving you, her home, and her parents. I have to wonder who is in that other country that is so important to her. Seems as if her immediate family is here. I know what she told you, but it sounds very fishy when she had an A with OM who she has known a long time and who lives there.
Be careful about agreeing to let her take your children, b/c there is a very strong chance that you would never get them back again. A year in the life of a young child is a long time to go without their daddy. If and when they do come back, you realize they will not be the same.
I understand trying to see her POV, however, you better be careful about letting her leave the country with your kids. I've seen women promise the LBH almost anything just to get to leave with the kids, and once that happened, he lost them for the rest of their childhood. Be careful about giving her sole custody....for whatever reason she gives you. Don't give that up. Get a lawyer, and don't sign anything she may present for you, until the lawyer looks it over.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!