Oh my poor dear lady. How truly awful.
Think about posting this in Living Overseas or post a link there to this thread, you might get some uesful perspectives.
I am an expat and I have seen marriages breakdown where the mother has to stay somewhere she is not happy. It is totally soul-destroying. Not only have you followed your husband to the other side of the world for his job, stayed when you had a really good opportunity to go back, because his needs were put first, you and the children have followed around after him and each time, you had to settle the children, set up home and start your life again while his job and career came first.
Now, he has, yet again, put his needs before you and the children and has clearly told you that you will not come first in his life and if you want, you can take the kids to the opposite side of the world while he sets up his new life. Neither you nor your children deserve this treatment.
You are in no way responsible for what happened, every time he put his needs before yours he took another piece of the relationship you built together and threw it away. This is his fault, not yours.
in 10 years time, you will have lived another 10 years in a place you don't feel happy, living on less income than you have now, facilitating a relationship between him and your children when he clearly has failed repeatedly to put their needs first. This will all come down to you and you will be left fitting your career in around your children and be left with a gaping hole when he can manage to waltz in and take the children away for a fun-filled weekend.
You will be 10 years older and lacking any energy to make a new start. Your children will be 10 years older and either heading into adulthood in whatever part of the world they want to.
Don't make any decisions quickly, but put yourself first. Get yourself a great lawyer and make sure you do not simply let him walk away from the lifelong sacrifices you have made for him and your family. Find yourself someone who will listen to you and allow you to work through all of your own thoughts, putting yourself front and centre, before you can work out what is best for the children.
Maybe you can get him to pay a lump sum for you to retrain / set up a business / throw yourself into your career while he has the children 24/7 and you see them every other weekend for two years and you can start the life you have never had the chance to dream of, as a xxxxx fill in the blanks. Maybe if you weren't traipsing around after him, you might be able to find happiness.
This would probably mean you won't then be able to take them to the UK at the end of it so if you really do want to come back, make sure your action plan will make that happen instead.
Tell your children you love them and that none of this is your fault and none of this is their fault. but that you will do your best to make sure you all come out of this as best you can. Make sure you are not the last in line.