Things to Bring-Bring a back pack for a diaper bag/park bag.
Use Gallon bags to keep things organized in said Park Bag. Diapers/wipes in one, snacks in another, and change of clothes in a third. It was so much easier to find what you needed in the bag quickly. And the whole bag didn't have to go to the bathroom to change a diaper.
Request a crib from Disney...they are usually pack n plays but those I have had are clean and they offer sheets too.
Make sure to bring a comfort item from home for sleeping, stuff animal/blanket. This helped my youngest this year.
Bring a stroller that has a good sun shade. We bought a new stroller and the sun shade is attached to the back so you cannot adjust it. Terrible design, i hated it for Disney. Our cheap umbrella stroller has a better sunshade!
A pop up hamper - this was the first time for this and it was a life saver! Saved spaced (not all the dirty clothes in a pile or in the luggage), but we got caught in a downpour at MK on evening. All 5 of us were soaked and our clothing (especially our socks) were soaked and stank. We did laundry that night and having the hamper was so nice.
Breakfast items for in the room in the morning. If you have a car plan on running to Walmart or Target for milk and food items. A few snack items to take into the park, baby food pouches, gold fish, veggie straws, etc.
ADR- Plan on eating at buffets. Buffet and family style meals (garden grill or Ohana for example) kids under 3 eat for free. Table service with a menu you share off your plate. I would still do character meals, Chef Mickey is a must for us. Though later in the trip to get the baby used to characters.
Driving - at 2 that is a little harder, but DVDs and a few toys. We drive at night so the kids sleep through most of the ride. Leave after dinner to avoid most of the traffic.
Rides - there are more rides that a 2 year can ride than cannot. Anything with a height restriction is a no, but otherwise you are good. At 2 all my kids like everything. Now that they are a little older (6,4,1) they are starting to be scared of Haunted Mansion and Pirates.
Play Areas - The is one by Splash Mountain under the train station especially for little ones. There is also a hidden one inside Mission Space exit at EPCOT. This one is for a little bit bigger kids but with adult supervision a 2 year old would be fine. There is also the dig site in Dino Land at Animal Kingdom that is awesome! And Hollywood Studios has the Honey I Shrunk the Kids movie set play area.
Packing - if driving pack items not in a suite case in boxes (like paper boxes) I used to pack the luggage with all clothes and then all extras would go in multiple bags. I was given the box suggestion and it was so much easier! We had three boxes, 1 for food, 1 for laundry stuff/toiletries/odds and ends and 1 for baby food/formula/baby stuff (our youngest was 1 this trip)