1. He refused to shake hands with their guests. He refused to sit and talk to them either. (no comma before either) 2. We can find a way that both of us can feel comfortable. (deleted "accept" as unclear; accept what?) 2a. We can find a way that is mutually acceptable to both of us. (mutual = applies to both parties)

I would say they are basically correct. Unlike the other two commenters, I am OK with the word "either" used as a sentence adverb. However, I would say "... a way that [we] feel comfortable WITH".

The second sentence is correct but the first feels a little funny. I would remove the word either and rephrase it. He refused to shake hands with their guests. He also refused to sit and talk to them. :) Hope it helps