Hi
Joshua! My family celebrated Independence Day in Magic Kingdom a couple of years ago. Yes it will be very warm, and somewhat crowded, but it won't be unmanageable. Typically my best advice is to arrive at the theme parks for the daily opening ceremonies, take a mid-day break back at the resort, then return to the theme parks in the evenings for dinner and fireworks. However, if you choose to visit Magic Kingdom on either the 3rd or 4th of July, I will suggest planning on getting there early and spending the remainder of the day. Magic Kingdom reaches capacity early during special holiday events. If your leave the park, or arrive too late, there is a chance you will not be able to get in to watch the special fireworks.
Traditionally, the 4th of July enhanced fireworks display, "Disney's Celebrate America: A Fourth of July Concert in the Sky" is shown. This is a 360 degrees fireworks extravaganza presentation featuring patriotic music themed to spectacular pyrotechnics. The special Independence Day fireworks display is generally shown both July 3rd and July 4th in Magic Kingdom. In Epcot you may experience the "Voices of Liberty 4th of July Concert" in the America Gardens Theatre stage featuring the Spirit of America Fife & Drum Corps and several Disney characters. IllumiNations Reflections of Earth will feature a patriotic finale. In addition there is usually a fireworks display with a Rock N' Roll soundtrack at Disney's Hollywood Studios. I will recommend visiting Magic Kingdom on the third and either Epcot or Disney's Hollywood Studios on the fourth.
Since your little princess will be celebrating her fourth birthday, let me suggest reading more about how to make her day extra special here. Enjoy the special Independence Day celebrations and your daughter's birthday at the Walt Disney World Resort!