Unfortunately, I've never affinity mapped so I can't really help you there. In regards to the rest, I don't think that there is ever a bad time to practice UX. I will prefix this with that I've never done UX for an event, but for a product, so just keep that in mind as a couple of things you may want to do differently.
The whole purpose and your end goal is to try and improve the experience whether that be for the kids or the volunteers. So something that you'll want to take away from all of your work are areas for improvement from your research and presenting those to leadership.
I'd definitely start with a mixture of interviews and surveying to get to know your users (whoever you're trying to focus on improving the experience for), what they enjoy, what they don't, figure out maybe any issues they've had in the past, maybe processes that they thought were successful or weren't; basically trying to uncover areas for improvement.
Here is a really great article on interviews and questions to ask (It's geared towards a product as opposed to event, but I still think it's relevant) : https://medium.com/interactive-mind/5-steps-to-create-good-user-interview-questions-by-metacole-a-comprehensive-guide-8a591b0e2162#.7uh7b3ntc
I'm not sure if you do these events frequently or rarely so you may want to skip these two next steps for time's sake, but normally from the interviews you would group information to create personas. You'll want one make one to represent each type of user or person involved in your event.
Now that you have your key people in mind, you can start to work on areas to improve. Create a customer journey map and go through the entire experience that each type of person has with the event from start to finish. If you're unsure, interact with people during the event. Watch them work and see where they struggle and where they don't. In your map, list any frustrations or successful moments that they might have. From this - come up with a list of opportunities to really help those 'low points'.
As I said, for time's sake you may want to skip the personas and the journey map and stick to interviewing / surveys and really just watching people work and how everything goes down.
It gets a little tricky putting these steps into action as you only have one week to work with, but if you have time, test out some of your solutions, see if the experience improves.
Definitely create a document with all our your findings so that they can be applied and tested in future events.