What you are doing has a pejorative name; It is called an info dump. Or alternatively, your barriers to entry are quite high or your learning curve is too steep to reach the lip of your barrier.
Now, you are not wholly and squarely within the info dump bubble, you're half way out perhaps if you believe this treatment on how to get out of it, but I would argue turning an info dump into "events" simply isn't enough. Before you continue, you need to know who your target audience is. Because if it's not your friend STOP. If your audience actually understands or needs this type of information, then you need to ask yourself a slightly different question and follow the path differently.
1 (See Link) Does It Matter; 2 How Much of It Matters; 3 Use an Existing Scene; 4 Or Create a Scene; 5 Don't Be Lazy
You say it matters because it's an explanation. You seem to think you need 3 new chapters to do the work. You think all of it matters. What you've done here is perhaps failed to execute on steps 1 & 2 & 4. At the very least, if your exception for audience applies, you've failed at step 4.
I find only the most pedantic of audiences care about your reasons for why something happens. They usually care more about the characters and the investment in them. The perceptions they have of those characters and their decisions. The events and reasons only get picked at when they are annoying, boring, or unbelievable. You've hinted that the last section may be unbelievable for your target audience. Which means you have to address the most common complaints with legitimate character foibles, interactions and development; not a treatise on how to correctly train people during boot camp.
This argument says that maybe you don't actually need much of boot camp, you should pick the small character driving elements of it, imply a lot and give an example for why this will work later while letting reader imagination filling in the holes.
Ok, I'm Wrong. You need Boot Camp for a very valid reason.
Well, you still need to make it interesting & your learning curve needs to be shallow enough to allow your target audience into your work and ensare them with the interesting things you are telling them. So, if your work is boring and hard to understand for your target audience you need to do a lot more work to figure out how to make your first three chapters interesting, not for the info they provide, but for the characters that are interacting in those chapters.
You sound like a plot oriented fellow. Hi, me too. I'm sorry you have this problem because plots are interesting to writers, but books aren't interesting without good characters & good character interactions for readers. Plots are not enough when you need to impart information. And people don't come to a pleasure read for learning (or at least, not many of them). You have to trick the reader and immerse the healthy proteins and veggies in something that tastes good.
Go back to the mechanics of good story telling and apply them to the boot camp. Give it a beginning, a middle, and an end. Make sure there is conflict. Make sure the learning curve is not too high. And, make sure that at the end of it all there's a reward: such as your characters having the realization that they are much better off than they thought they would be or some other such reward that clearly directly comes from their training. Along with that reward, you need to have a further complication (they must go to war) that appears to have serious ramifications for them all (that they might very well die).
A final hint for you: You are writing an underdog-sports story, aka air-bud. Your team has to be interesting. How they get together and bond has to be interesting. You make the team sympathetic, the thing they must conquer scary and huge. And then the reader magically cheers for them when everything comes together (of course it will) at the buzzer. You can take all sorts of archetypal events from the sports movie genre to spice this up, and you'll be in good company.