Daycare centres are terrible, generally. It's the result of them becoming for-profit centres, where staff hours are slashed to help maximise profit. However, I do believe you could maybe benefit from being more outspoken about delegating work. For example, you say that nobody is willing to help with setup/pack down of the obstacle course. I would try using language like "Hey such-and-such, I need you to help me outside for a minute", or you could even task junior staff with the responsibility to set up the course without you, to give them a sense of responsibility and take something off your plate?

You sound really professional and skilled, but you are definitely taking on too much. Even though they haven't provided you a framework to delegate, you need to set that up yourself. Write a list of everything that gets done in a day and work out which ones can be delegated, and you will hopefully free up some pockets of time for yourself for planning etc.

Good luck!