Two of our daughters married Americans and decamped from home (Malta) to the other side of the Alantic. At first I did find it hard and of course missed them. However, we raised them to be be independent and to follow their dreams, so we're quite happy that they had the guts to go and give it a shot.
We also had some very lovely and memorable holidays in the States which, I am quite sure, we would not have had if not for visiting our children.
When our only DGD was born, I was fortunate enough to go and see her enter the world, and we did a lot of skyping between visits so she always knew who we were.
Time has moved on,both daughters divorced, one still in the US, the other has returned to Malta with DGD ( aged 4). Although delighted to have her here, especially since DH's death eight months ago, I would far rather she was still in the US with two happy parents, but it was not to be.
Be happy for your children, trueblue. We only get one shot at life and if they have the opportunity to experience living in another country they should do so without having to be made to feel guilty. I do sympathise, believe me, but lots of us have had to deal with it and you do get used to it.
I wish you all the best 