If an email correspondence between you and a coworker has gotten a bit tense or catty, it's time to move this discussion out of the virtual realm and into the real world. If you can't meet with them face to face, at least pick up the phone and give them a call. It's important for them to hear the intonation of your voice, but it's just as important for you to hear their voice. You may have made some assumptions that just aren't true. Things are not nearly as bad as you think.