I had a similar overly-sensitive colleague. (She was support, and would get flustered at my short responses like "please file a ticket" or "logs.")

She left the day after I met with her and explained common sense. (Customers expect you to know how to use the product; don't bypass the ticketing system by emailing me directly; follow the documented process to escalate to engineering; don't just copy and paste customer emails without doing your own investigation...)

I was having a lot of trouble with getting my manager to intervene with her, so in this case her departure was a godsend. We ended up firing my manager a little later, and things ran so smoothly afterwards that I realized he was the real source of the problems.