Milk should be available on site.
Ice water can be had at most anywhere with drinks. It is a small cup, but you can ask for two. I brink flavored drops because I do not like the taste of the water.
I see no reason a 9 year old couldn't be responsible for his own lanyard. It is not like on a cruise, where you only need it occasionally. He will have to show it for each ride. (twice)
If you have trouble on a ride, just shut your eyes until the ride stops. I don't think it is the motion that get people, it is the visual added to the motion. The only ride I have trouble on is kracken at SW. I still ride it, but with my eyes shut. Otherwise I come off so dizzy, I almost fell down the steps once. No dizziness now.