Is it assur to walk to shul in the rain on Shabbos? You get wet. So you don’t squeeze out the water. Sprinklers are a vochedig activity, and though it might not be halachically an ISSUR to get wet, it still encourages the kids to do things that should not be done in the spirit of Shabbos.
I thinks it would be better to find another park, or not take the kids to the part where the sprinklers are situated. One could say that sliding down a slide is also a non-Shabbosdig activity, but I don’t see any parents not letting their kids do that.