when you saw them turning cars away, was it later in the afternoon? So your telling me as long as we're there when the gates open at MK on July 4th, and we don't leave... we would be ok? Cause that's what we'd do if we had to. Would the other days that week, (the 1st, 2nd, 3rd and 5th) be better probably? I'm sure most people go to MK on July 4th because of the fireworks show. Should we be able to leave and come back on the other days? I'm trying to decide if we should bother with the hopper, if we are gonna be stuck at a park all day.
How do the fast passes work? Can you explain them to me?
We usually leave the park around lunch-time, between 11:30 & 2:00, so that's when we saw the cars being turned away. Yes, only on July 4th have we actually seen them do this. I am unaware of any other days or parks that were closed due to capacity. On other days, we have left & come back or switched parks with no problem. We always go that week!
I would think as long as you are at MK when the park opens on the 4th, you'll be fine. I don't know of Disney ever "kicking" anyone out once they're in! I can't imagine anything like that!!!
FP - go to the ride (Splash Mtn, Space Mtn, Peter Pan, etc.) that you want & check out the stand by line. The wait time will be posted above the line's entrance, so you'll know how long it is. Right beside the stand by line is an area with FP Machines (sorta like a funky ATM). Above the FP machines is a clock that will give you the "window" for FP return time (ie 12:15 - 1:15). You simply put your park ticket - one per person - into the FP machine & it spits out a "voucher" with the return time printed for that ride! Fast, Simple, Painless.
FP Tip #87 .... You do not - I repeat you DO NOT - have to return in the specified one hour time frame to be allowed admittance to that ride!!! We have tested this NUMEROUS times. As long as you return AFTER the beginning time on the FP, you will be allowed in the FP line for that ride! DH didn't believe me when I told him this, so I've enjoyed several "told ya so"s from this trick!
Another FP trick to remember .... you CAN hold multiple FPs at one time! Disney originally did not allow this, but now they do! When you obtain a FP, the ticket will tell you what time you can get another one - usually 5 mins after the one you're holding goes into effect.
Example: You get a FP for Splash Mtn that says you can ride between 10:15 - 11:15. At 10:20, you may get a FP for Big Thunder Mtn & it may say you can ride between 11:45 - 12:45. Now, at 11:50, you can get a FP for the Haunted Mansion .... and so on..... Important to remember: YOU DO NOT HAVE TO USE THE FIRST FP BEFORE YOU GET THE OTHER TWO. You can have five (or more, in theory) FPs in your hand and go around late in the day popping right on the rides! We have been known to grab a FP for Space Mtn when the park opens, hop in the standby line (because it's not full yet), ride the ride and come back at night to use the FP we got that AM to get in line while everyone in standby waits 2 hrs! THAT's what I mean by "working the system"!

Our kids think we're the best!!!
I apologize for the length of the reply - but I hope it helps!