When my DD said she wanted to pitch I immediately got her lessons from an IR pro. She quickly showed progress, and her passion to pitch and play grew concurrently. So I caught her (and still do) regularly, sometimes reminding her what her PC said to work on.
But from Day 1, I began talking to her about composure in the circle. Don't let the other team know when you are rattled, or you're done for the day. It's a lot easier just NOT to get rattled. Focus your thoughts on your next task: the next pitch.
Here we are 4 years later. I guess I said the right words because she has great composure, whether she is doing great or getting rocked. The other day after a game I asked her if a routine play error by her 2B, that put the team in a bind, upset her. She told me she was totally pissed. I was so happy and I told her I couldn't tell. I told her I know her better than any of her teammates and any of her opponents, and if I couldn't tell she was pissed, neither could they. Fantastic composure.
So keep trying to find the right words that click with your DD. So important. I guess I got lucky.
That is exactly how I want my girl, even if you are upset never show it, and use it as motivation. Like someone else said a rattled pticher is like blood in a pool full of sharks for hitters.