With little ones the morning EMH at Magic Kingdom may be worth it, as Fantasyland is open. But be aware that morning EMH at the other parks have limited open attractions, and many of them are the things that your little ones won't be riding. May not be worth it.
Also, consider if you're going back to a park after your break or not, and what your touring plan will be for the evening. If you aren't going back at all, then EMH at MK totally makes sense. If you are hopping to another park, realize that you won't have any Fastpasses for that evening session. So make sure the stuff you want to do is "filler" stuff i.e. not headliners, or maybe you just want to stroll around Epcot World Showcase? If you are going back to MK in the evening, gather as many Fastpasses as you can in the morning, and use them when you go back in the evening. This is the reasoning for not park hopping, by the way. Also, if you don't go to EMH at all, and you collect Fastpasses diligently, your experience after going back for the evening session can be greatly enhanced by not having the EMH crowds there, and by having a fist full of Fastpasses!