While each child does need his or her own Express Pass printed, when my kids were quiet young, I always put both of their Express Passes in a pouch and carried them with mine on my lanyard. Then they just scan me 3 times when we get into lines. Last year, I finally decided it was time to let them try carrying their own EP in their lanyard and wouldn't you know it my son (7 at the time) took his slytherin lanyard off in the bathroom and it wasn't until we were in line for the next ride that we realized it wasn't on his body. We went back to the bathroom immediately. It was already gone. We went to lost and found in front and someone had brought it up there already. However, they had found it IN THE TOILET so we had to reprint our EP. Which was not as huge of a hassle as I worried it might be. We're going back in June and I'll try again to let them carry their own. But if you don't want try that then I'd just put each pass in a plastic lanyard pouch and carry them all with you. That always worked out just fine for us.
I might bring some packing tape this time around and kind of laminate ours a bit too. We rode quite a few water rides in a row last year and the EPs got soaked to the point that they wouldn't scan even thru the plastic lanyard pouch. We hit the water rides pretty hard that day!!!!