Some teacher or something told me that my daughter couldn't use the playground until 225pm after school is out. Does she have any power to tell me to leave? As far as I know, this is a public park.

No power over the park but yes for the school grounds.

This is a public park. However, I believe there is an adjacent playground that is for the school. As long as you were on the side of the park with the boat and whale tail I am not aware of any reason you would need to leave. That's odd.