Sucks, doesn't it?
You gave them life, raised them to be ambitious and successful - and then they were ambitious and successful and that took them off to a faraway locale or even over an ocean. Then you realized what you really wanted was for them to be ambitious and successful...at something that would have them living right next door to you. Oops.
But they're there now. They are happy. They love their new city/state/country. They've settled in and are enjoying the fruits of their labor in the place where they are. Would you have them compromise their happiness and success to live next door to you?
If you would, is that really love? Or is that actually a bit cruel? How would you feel if they did compromise and were miserable with their new life?
How to cope when your child is happy abroad and you kind of wish they weren't:
Skype/Facetime/Telephone: Old tricks, but good ones. If you both have Skype or Facetime you can talk every single day with video - FREE. Every single day if you want! You can see your child's every haircut and zit and new outfit, if they have kids you can see their every new skill and school project. But don't spend those conversations complaining about where they live or they might not want to have them as often as you do.
The Mail: Everyone loves mail. Send packages back and forth with your kids - foods they like, news clippings from home, books you enjoyed and want to pass on, fragments of your daily life that you wish you could share with them but they don't live next door but oh wait, the mail! You CAN share them!!! And in return you'll get exotic goodies and bits of their life back from them. If you can't afford to ship gifts, how about letters or homemade postcards? Have we all forgotten how fun those were? Definitely always a good idea. Don't spend the letters complaining about how sad you are that they don't live next door. You can talk about that to ANYBODY except your kid, ok?
Take Cues From Them: Wow, making your life as an adult in a brand new place is no mean feat! Many a depressive phase has started out that way. But somehow it seems your kids have done it in a foreign country and even found happiness that way! Dang! How did they manage? Take cues, and their routes to happiness might work to help lift you out of your my-kids-are-too-far-away doldrums, too. Did they volunteer? Get a job they really enjoy? Join a church? Go to pub quiz every week? Start a garden? Make a point to go for long walks in the country every weekend? Give it a shot! You'll be too busy to care where the heck your kids live!
Visit: I bet your kids visit you. At least once a year, they shell out thousands of dollars for plane tickets, airport food, rental cars, and all the other horrific and sometimes anxiety-laden trappings of international travel. In return, do you visit them? Or do you seek to "punish" them by refusing to visit or by complaining that their trips are not frequent or long enough? Do you believe that since they do it every year, thousands of dollars must be nothing to them? I bet it's not nothing. I bet they work hard to make sure they have that money to spend on you. They are paying their dues for living abroad in this way. If you cannot find it in your heart or your wallet to visit them and show interest in seeing the new lives they've made, the least you can do is not lodge complaints to them about how they aren't doing enough. You can call up your best friend for that.
You're Not Going to Make Them Move Back: If you've tried all of the above, or refuse to, just at least try to understand one thing: they've already made their move. If moving back was just a matter of a few simple parental complaints, it's unlikely they'd have ever had the nerve to move abroad in the first place. It only makes them dread conversations with you, which is exactly what you and they don't want. Yes, they do understand that everyone dies. Which is why they don't want to spend their precious conversations with you talking about how you don't like their life. Even if you think you're doing it in a "joking" or "loving" way.
Do your kids live abroad? How do you cope? If you live very far from your parents, how do your parents cope?