Oh my god, this sounds like my worst nightmare. This past summer I worked a job that involved making a ton of phone calls, but luckily, I was in a separate office from my supervisor, so the only person listening in was my co-worker who shared an office with me, and even THAT stressed me out a lot. To be fair though, I doubt the "coach" in your situation is going to tell you to stutter less, or if they do, it would be in nicer terms than that. I have been in work situations where my stutter has gotten in the way, and people will find the nicest ways to get around having to tell you to be more fluent. They might tell you to "speak slower" or "just relax" before they tell you to just straight-up stop stuttering.