Hello Joyce and welcome to the Disney Parks Moms Panel!
WOW! All four Walt Disney World theme parks in ONE day. Now
that is an ambitious plan.
You are correct, the
FastPass+ system allows you to make three selections for each person at one park, to begin with. Once those three FastPass+ selections are utilized, you can then add another FastPass selection. Once that is used, you can add another and so forth. However, there are a limited number of FastPasses available for each attraction. It is not uncommon for all FastPasses for popular attractions to be gone weeks before any given date. Even less sought after attraction FastPasses are often distributed entirely by midday.
Since you are hitting the parks the day before the Fourth of July holiday, I would expect the parks to be hopping and low FastPass availability. If you are not Walt Disney World veterans, my advice would be to choose only two of the four parks to visit. I would make FastPass+ selections for the afternoon at the second park and hit the first park well before opening with the goal of riding your top three attractions at that park first thing. Another option would be to explore one park more thoroughly. With the age of your children, I would select either the
Magic Kingdom or
Disney's Animal Kingdom. But, you will have a fantastic experience whichever parks you choose to visit.
If you have more question, please come back to the Disney Parks Moms Panel. We would love to help you plan a great day!
See ya real soon,
Anne