You cannot create an event program within an event program or even a default program. We host similar functions at events. We have always used separate events for each "event".
I tried this on 2 devices, an ipad and a Samsung Galaxy. I was able to access the events at the same time and check people in. I am not sure if there will be any unforeseen hiccups...
Gary is right about creating some sort of trigger campaign in the future. You could have have a flow step that date stamps a field possibly.In this case, it sounds like you are try...