Hi Larissa:
WIth a large family with such young children, I'm not certain that a
park hopper is necessary as it may be difficult to take advantage of park hopping with young children who may need naps or may not be as interested in being as aggressive in seeing everything.
The park hopper option may be handy, however, if you decide you want to eat at restaurants in other parks than the one you plan to visit that day.
You'll probably find that parks are not as crowded right at opening, and you'll probably be able to take in a ride or two with little wait if you arrive at Park opening. After lunch, some families return to their Resorts to relax, nap, or take a swim. However, the Parks won't empty out, you'll still notice crowds.
Enjoy your vacation.