Hi Tammi,
I think that with a few tricks, you can have a great day with your little ones at Magic Kingdom.They are both young enough that they will be "Mickey Mouse's guests," and thus not need theme park admission!
First of all, yes, bring your double stroller if you have one. You can
rent a double stroller at Walt Disney World; however, if you have one that you know your children are comfortable in, bring it with you. Magic Kingdom is very stroller-friendly.
I suggest that you arrive as early as you can on the day that you plan to visit. Crowds tend to be at their lowest, and many children at their happiest, early in the morning. You can take in many attractions in the morning hours, concentrating on Fantasyland, which has attractions that are especially good for little ones, such as it's a small world. I suggest that you make a reservation for lunch, as this will be a good way to take a break in air conditioning. One of my favorite restaurants at Magic Kingdom, and a hidden gem, is
The Plaza Restaurant. This low-key eatery features classic and delicious fare.
I suggest that you take advantage of the
Baby Care Center while at Magic Kingdom. The Baby Care Center offers a cool, calm place to feed, change, and simply take a break with your little ones.
As to parades and fireworks, that is very dependent on your children. If they enjoy watching colorful entertainment, they might love these. If they are during a typical naptime or if the fireworks are too late, you might consider skipping them.
I would love to help you plan more Tammi; however, I am limited in the space that I have to answer. Please let us know if you have any further questions!