Michelle,
Like DH said it's not personal. The DI probably wasn't really in a bad mood, just trying to reinforce for all, esp. "Nature Bar Boy" that you don't break the rules. When you are told to do something, you do it. When you fail to do as told, sometimes others pay for your mistake. Also a lesson to his platoon mates. His battle buddy, squad members, etc. should have stopped him. Group punishment like this is just the way they do things in Basic.
DI's always find SOMETHING-- footprints on the floor, soap film in the shower, etc. and whatever it is will be the End of Life as We Know It. Honestly, probably had to do with it raining. had to cancel training. What can we do with the Trainee's for 8 hours.
As for Family day, don't worry (I know you will anyway). The DI could cancel Family Day, but it is doubtful. (don't tell your son) Usually, cancelling something is a threat that they have to hold out there to improve behavior. (What are you going to do: shave my head, make me wear green, and keep me in the barracks area? I'm already there)
Things will work out. Try not to let it upset you.