Be strong - you have made the decisions for the best reasons for your family. Yes, they will be devastated but will, in time, learn to live with it and hopefully understand why you have chosen to emigate.
I speak as a parent who was quite ill for 2 years with stress related conditions leading up to my daughter leaving and until I was able to visit them all and see for myself what a great life they now have. I kept this to myself as much as I could as I didn't want to make their move any harder than it already was. I'm fit and well now and glad they are happily settled and living their dream.
6 years on we are nearly at the end of the long process of getting a parents Visa and should be living nearer them all by Christmas. Not eveyone has this chance I know.
Be firm, tell them you love them and pray that in time they will accept your decision and support you. Don't give up on them - they are hurting right now. Make sure they have access to a computer and know how to use a webcam before you leave - that can make a huge difference. Good Luck.