Hi, Kim! Having kids sure does change everything, doesn't it? But I can tell you, having traveled many times to Disney before I had kids, you will see it in a whole new way once you have your little ones tagging along!
The first thing I would get is a backpack that is comfortable to carry and that is roomy on the inside. Keep an extra set of clothes for each child, juice boxes, goldfish crackers (or some other snack that won't melt), sunscreen, wet wipes, autograph books, pens, hats or visors, and sunglasses if they will wear them. (I know it seems like a lot, but you will need all this stuff!)
I would also carry a small diaper bag. That way, if you have to run for a diaper change with your little guy, Dad can stay with your daughter and the big bag, and you make the diaper change without carrying so much.
Baby Care Centers are located in each park, and they are the best you will find anywhere. They are clean, and have everything you will need: changing tables, rockers, rest rooms, extra baby supplies and more.
Strollers are available for rent, but they are pricey at $31 per day for a double. I would bring a stroller from home. With the ages of your kids, a stroller is a must!
Finally, don't forget your camera. You will want to capture all the magic! Have a wonderful time with your family!