Back in the 1950s or 1960s, little consideration was given to the giving private places to pee or poo to school kids. I doubt it ever even entered any adult's mind. And thiis was not limited to preschoolers or young kids.
When I was about 10 or 11, one day I was feeling pretty sick. The teacher noticed and, as was standard practice, I was sent to the school nurse. Tye nurse's office was on an upper floor of the school and had her office, three small cubicals with a cot and sink in each, an a toilet in a 4th cubical. All the cubicals had curtains across the front, but no doors, Everything that went on in one, could plainly be heard in the others.
Anyway, after a quick temperature check, nurse told me to lie down in one of the cubicals and said she'd be back in a few minutes after finishing with another boy. I took off my jacket and laid down on the cot. After a couple of minutes, I saw the nurse walk by to the cubical next to mine, carrying a white irrigating can, with the hose draped over her hand. The kid next to me started to protest as soon as he saw her walk in, but there was no arguing with her.
For the next few minutes, I heard the unmistakable sounds of a big enema being given and the recipient complaining about the fullness and cramping.. Then nurse said, OK, you can go to the toilet now and the kid scrambled to the toilet. I could clearly hear the enema working.
Soon, nurse came back in to see me and said she'd called my mom and they'd agreed I should go home early because it looked like I was getting a cold, so left. I never did learn who got the enema, but it sure sounded like he needed it and it really worked.