They are at the edge of divorcing. - I understand this and it's grammatically correct, but it still sounds odd. I might say "They're right on the edge of divorce./They're ready to be divorced." I ate too much to stand up. I am too stuffed to stand up. I am too tired to stand up. - Sounds like my life! :) Yes, these are good.

I agree with Georgia. You might also say, "They are on the edge of getting a divorce." or "They are on the edge of a divorce." I agree the rest of the sentence sound fine.