I agree with the opinions posted, in general, but just wanted to point out that according to her post, his kids are in the UK. So either way, someone is going to be making a very big sacrifice.
You know, I've been thinking about this kind of thing lately because I read lots of stories on here, for better or for worse, and as much as I want everyone to be happy with the person they love, I think sometimes you have to say "I love you but the circumstances are not right, therefore we can't be together"
Lots of people on here assume that their relationship has to work out because they're in love, but I don't think that love is enough when you're in long distance. It takes a ton more commitment, trust, sacrifice, pure effort, work ethic, time, energy, forgiveness etc to make a long distance work successfully than one where you're in the same environment. Also if you read the re-pat board etc, you'll soon realise that the troubles do not end when one person makes the move, it is in fact where troubles begin. As a cross-country couple you have to be prepared to deal with, drop in income from moving countries, missing friends and family, cultural differences, sudden change in lifestyle, etc for a VERY long time, you may never be 100% happy as someone will always be away from where they consider home to people. Many people will find home in their adopted country, but many will not.
Your relationship is further complicated by the fact that wherever you, there will be children missing a parent.
Lots of people on UKY are willing to put all this effort in and reap the fantastic rewards of moving and a happy marriage, but many people are not willing to go the extra mile or it's not appropriate for them to.
If you want my honest opinion, what I'd say if I were you... (you may want to stop reading now)
"I'm sorry but I'm not prepared to leave my daughter, and I would not want to be the person that took you away from your children, therefore I can't see a future for us as a couple"
And I'm sure my heart would break as I walked away, but you know, some things, like your children, are more important than a broken heart.