How do you cope with unforgiving family members?

There was a possible miss understanding on my part all though I will never know because my sister and mother wont talk to me anymore. I sent her a very frustrated email that i'm sure was very offensive. A while later I tried to apologize for it and make things right but they have shut me out completely. They have even shut my son out that was very active in their lives and he had nothing to do with it. What am I to do when I keep making attempts to apologize and no one will accept.