I'm so sorry you had this experience OP.
There's absolutely no way I would have either forced a move abroad or left my child with family at that age.
At 15/16 children are on the brink of adulthood and need good parenting more than ever.
They have pressures of exams and of making life changing decisions without the maturity or experience to understand some of the repercussions.
I was so sad to read the comment about "get a job" when you had no money.
Yes - it's good for children to earn "pocket" money but not to pay for basic items and at 15 they are still a child.
To answer your question, I'd have stayed in the U.K. with my children and provided stability whilst DH worked abroad.
I'd have worked out with DH how we would manage visits as often as possible and found a way to make it work for a few years until my child went to Uni.
I'm not surprised you feel upset, maybe even resentful.
I'm not a perfect parent. We all make parenting mistakes, but leaving a teen at a vulnerable age is not an arbitrary error of judgement.
It's bloody shitty, selfish parenting and YANBU to tell them that.