From everything I've read, the most crowded day at MK is Monday. So we've avoided it on Mondays and and found the crowds to be more tolerable.
Guess it also depends on the ages of the kiddies. If they are so excited and want to go to MK first, then as suggested above, go EE and leave around lunch and if the crowds are too much, switch parks in the afternoon/evening. We always go back our last evening for the parade and fireworks. They are truly wonderful and a terrific way to end the vacation.
Have a great first vacation!