I can see viewpoints from all perspectives (yours, your wife's, your children's & your gf) and can give you advice on it all if you would like.
I think you've had very fair feedback given to you from everyone on MN.
I have 3 young children aged 4 and under. I am married but have been a SAHM which is extremely hard work and I now work full time which is also hard work.
If you want to private message me I can give you an honest perspective of what caring for your children is like, day in and day out, for your wife vs what your life is currently like.
I can also help you think about how you would like your life to look living back in the UK if you were able to afford it and how that would look for you and your gf if you're still together.
It's all about compromise. Your children do need you and you have to be realistic about if you really want them in your life and what that looks like going forward. The worst thing you can do for them, is give them snippets of your time, as they will resent you forever. Especially, when they grow up to learn how you hurt their mother too.
You can turn all this around if you're willing to but you have to be honest if you really want too? Did you ever really want children? Are they better off with you in their lives or without you but financially supporting them from afar which is what you've been doing so far by the sounds of it. A lot to think about and you really do need some honest straight talk looking at all perspectives.