Sorry I'm a bit late joining this discussion, but I've only just become a member.
In 2014, one of my DDs emigrated to the USA with her family, when her husband changed jobs. I still miss her unbearably, and her kids - 2 boys aged 11 and 20, 2 girls aged 18 and 4. Before they moved, they always lived near us and we saw them regularly.
I'm lucky that my other DD and SiL live with us, so I get to spend lots of time every day with their 2 little girls, aged 4 and 6. They have been a huge comfort to me. However, I still feel the loss of my other DD and DGCs. We talk to our DD on Skype, but the kids just drift by the screen and wave to us. We understand that talking to Nana and Grandad isn't their top priority.
I try to get on with my life but sometimes the sadness overwhelms me and I have to cry. To make things worse, I can't really say what I feel. We always supported their move, even when our hearts were breaking, and other people always say, "Oh, you wouldn't want to hold them back. It's a great opportunity for them." Yes, I know it is, and I can see they've got a better standard of living, thanks to Sil's new job, and have thrown themselves enthusiastically into the American lifestyle. Of course I want them to be happy. I don't need people to tell me I should want that! I just wish they were being happier closer to home, not 3,000 miles away.
My other DD is wonderful but gets upset when I cry for her sister, because she feels I'm not appreciating what I've got, i.e. her family. My DH misses them too but keeps saying, "We'll go and visit them", which isn't realistic as money is tighter and will only get tighter when he retires in 2 years time. There's a little part of me that is angry at them for moving so far away from us, though I know it is selfish and makes me feel that I'm a horrible person.
Sorry about the long post. I just needed to get it off my chest!