The UG is all about doing it ALL in one trip. And you can't. So don't think you will. Building that time in to just stop and explore is really, really important. One of my older DD's fav things at the MK is looking at the display windows on the stores along Main Street. Each window features a different princess. We have to stop and explore those windows every trip. That's part of the magic of WDW for her, but you won't find that in a guide book. I think you need to let kids "find their own magic" like that.
Also the UG is about seeing and riding EVERY ride and attraction. Your family may not want to do that. There are plenty of rides/attractions we've never been on and have no desire to see. I culd never ride the Tea Cups and be fine with that LOL! Sarah still doesn't like the Snow White ride, so we skip it, etc.
Each park does rope drop slightly differently. Generally, they start letting guests into the park about 5-15 minutes before the park actually opens. I *think* its when the crowd milling around outside gets to be too large to manage. Some parks (the MK and AK) have a little 2-3 minutes show the characters do at the opening. So they let you inside the gates, but they keep you contained in the very front area of the park. At the official opening time, they literally drop the rope and let you in. But no, you can't wander around at will in the park.
If you want to wander around inside the park early, the best thing to do is to have a breakfast reservation before the park opens. Then you can wander around a little, but nothing is open except the breakfast restaurants. But you can look at things outside.
Touring with kids those ages is hard I think. I would consider splitting up and sending the younger two back to the hotel for a nap and staung in the park with the 5 year old. But I think you may find that even the 5 year old needs a rest after a couple days at WDW.
What we usually do is arrive just before opening to see the ceremony and ride most of the rides we want to ride before lunch. We have a snack around 10/10:30, and then a sit down lunch around 1/2, see the parade and then leave the park. We go back to the hotel and rest at that point. We often go back to a different park after that for dinner and more (slower paced) touring. Epcot is particularly good for wandering around after dinner.
Beth, mom to older DD (8/01) and younger DD (10/06) and always missing Leah (4/22 - 5/1/05)