Hello, Jessica!
I am so happy that you are back with more questions!
If you are planning on adding the Park Hopper Option to your non-expiring tickets, here's what I suggest:
Relax and enjoy your resort that first day / night. The pool at Bay Lake Tower at Disney's Contemporary Resort will easily occupy your day; considering booking Chef Mickey's that night, so your family can enjoy a great character meal right next door to your studio!
On Tues, 5/7/13, head to Magic Kingdom as early as you comfortably can and plan to stay through lunch (if you do add the Dining Plan, use those
dining suggestions we talked about earlier) then either take the monorail or a very leisurely 5-10 minute walk back to your resort. Let the little ones sleep as Mom and Dad enjoy a relaxing chat on your balcony (or a nap, too!) Then, shower / bath and head back to Magic Kingdom for nighttime festivities!
Wed, 5/8/13, sleep in a little; it's your second day in MK, and you can head in when everyone is ready. Enjoy rides you missed the 1st time or get a second ride in! Consider a Table-Service meal at a MK area / monorail-accessible resort this night. Ask for suggestions on this one!
Thurs, 5/9/13: Epcot, where there are so many hands-on experiences for your
kids and wonders for the entire family to enjoy. Consider using your
Table-Service entitlement here for either breakfast or lunch, since
there are so many fabulous restaurants to sample here. Head back to BLT after you have eaten lunch; nap / swim and decide if you're up for a park or would rather relax at the resort that evening.
Don't forget a trip to Downtown Disney! (That requires a question unto itself)
Hope this helps! Send more questions! :-)