4th of July is busy but we didn't find it overwhelming. I'm not sure how it compares to spring break as we haven't been during that time frame. As for the stroller, it was a bit trickier later in the week of Christmas week but still doable. I have never had an issue with the stroller 4th of July week.
Let's see tips I have...
those spray water bottles with the fans! 1 for each person no fighting that way!

I usually pack some of those quick dry swim trunks/rash guard shirts. This way I can let the kids play in the water at Epcot for instance but they dry very quickly.
We usually plan a break so that we can go back and clean up at the resort if we have a dinner ressie. Makes us feel better to not be sticky and yucky at dinner and then we are refreshed for the night at the park as well.
How many days do you plan on going? That will help think of other things as well.