it is suggested that you avoid the park with EMH. Some days two parks have them...one early, one late. The thinking in the guide book is that EMH causes people to be drawn to that park, so it becomes more congested than usual.
I've wondered about this, too, as there used to be set rules about which days which parks were busier, but I guess with the EMHs moving around, you can't go by day of the week anymore.
BTW, don't count on the kiddies leaving, lol. If many families are like mine, the kids would rather play than sleep anyway. One of the days of our trip MK is open until 2 am for Disney guests. My 12 year old is saying he wants to stay until closing. I told him maybe 12:30 or so...if we stay later than that the younger one will be totally useless the next day.