I'm reaching back in my memory (not to far, but far enough) to answer that question. We did a drive from Massachusetts down to Disney in a camper when I was a teen. I distinctly remember that as soon as we arrived at Fort Wilderness and got the camper hooked up, we kids went one way and my parents went in the entirely opposite direction. We were just so excited to be #1. out of the camper and #2. at Disney World, that even though we didn't go into the parks, we took off and road the monorail through the hotels and by the Magic Kingdom and then hopped on the Epcot monorail and rode on that one around the park and back. That seemed to work perfectly for us. We returned to the camper and made peanut butter and marshmallow sandwiches while waiting for my parents to return from a much needed, quiet dinner and a few glasses of wine I'm sure. The rest of the time, we basically did our own thing in the mornings and made plans to meet up in the afternoon.
Now with my kids getting older, I find that most mornings, we're on completely different schedules. I like to get up early and get on with things, while they tend to sleep in, shower, hair, make up rituals, etc. By the afternoon though, we're all up and out and it's just easier to make plans for that time. Last summers trip to WDW was fun with teenagers. I told them that they could do their own thing at times, but that we also had some family things scheduled, like Cirque de Soliel. We'd map out our plans for the day and also a time and a place to meet, but funny enough, almost everytime, my cell phone would ring well before our scheduled meeting time and it was my teenagers hoping to catch up with us early. I have to say that Disney was a magical place when I was a teen and it's been just as magical now that I'm a parent with teens. It just has that something special that draws families together.
Have a wonderful and safe trip.