As far as Peace Corps is concerned, my Mom had a cousin who did Peace Corps back in the 80s so it wasn't a new idea. She always spoke highly of him and his service.
As far as the distance is concerned, my family was used to me coming and going. I had already spent time away in Germany so they weren't new to the idea of my being over and ocean away. My family was used to me getting wild ideas in my head and then following through with them and then not seeing me for a while.
I have had some people tell me they were envious of the opportunity I have to experience a different culture in this way. I think overall they were excited for me and very supportive of my decision.