My daughter was in the exact opposite situation. She was a Jr. and there were a Sr. and sophomore pitcher as well. The difference between them was small. My girl was probably a little faster than the other two (62-63 vs. 59-60), but all serviceable pitchers.
My daughter started the year pitching every inning. They played a tournament and she pitched 3 games in one day (234 pitches) early in the season. She got a blister on her finger and on her plant foot. Her shoulder was sore and she was pitching like crap in the last game.
I asked the coach why she wouldn’t put the other girls in. I explained that we needed them to be ready and they need innings to be ready. The coach then said, she was going to play the best 9 in whatever position she wanted and she would not discuss playing time (she didn’t know my daughter was the one pitching every game). I then explained who my daughter was and that if she put her on the rubber for the games the next day we were going to need a private conference because she was hurting her.
On the bus, the coach talked to my girl and said she was sorry for pushing her too hard. The next day both of the other girls pitched and we won both of the games.
The rest of the season they got to split innings and they performed way better as a team.
Moral of the story is a grown up conversation might help resolve some of the issues. Girl pitching every game probably would like some rest as well.
This is a very different situation. You were not discussing playing time. You were expressing concern over your daughter's health/overuse, and while the coach should obviously have not needed that conversation with you to figure it out, notice how once you made it clear what the issue was, she went from "not discussing playing time" to immediately handling it?