The showers are separate stalls- it's not like you're all standfing around naked together. Pics of showers posted in first post at
this site.
I doubt anyone will object to your bringing your six year old grandson in with you. I've done it many times with my grandson at State Parks. I did always have him stand outside for a moment so I could check and make sure anyone inside was "decent" and O.K. with the idea.
I say "did" because he's ten now and old enough to go inside and use the (separate) stalls in the men's shower by himself- with me standing just outside the whole time, of course. Only problem with this method is that I have no way of knowing if he actually used the soap, or just got it wet enough to make me think he did! :B