Tampa-San Francisco: First family road trip - any input appreciated

Hello,

I am so glad I have found this forum. All the information I have read so far have been very useful, thanks!
We are a family of four and are planning a family roadtrip in the US for the first time. Our kids are 6 and 9 and last year we dragged them through 4 countries in Europe (we are experienced home-exchangers), so they are accustomed to being on the move :). So my initial (not exactly developed) plan is a one-way cross country road trip in June/July. We have approx. 3-4 weeks. I was thinking going on the southern route and include some or all of these stops:
Tampa (where we live)
Panhandle (Panama City), Fl
New Orleans
Huston
San Antonio
White Sands National Monument
Tuscon
(Phoenix)
San Diego
Joshua Tree National Park
Yosemite
San Francisco
We would rent a car for one-way and would fly back from SF. We would sleep in motels or campsites on the way.


My questions:
Is this a fun, educational and interesting trip with kids? I am sure about the national parks, but what about the cross-country route in the South?
How about safety? Do we have to worry about certain areas or being on the road with the kids?
Is there anything along this route that is an absolute must? We love the outdoors (nps, hiking, kayaking, biking), experiencing different cultures, and I am a photographer - as far as our interests go :)
Is this trip doable without spending way too much time in the car? I was thinking driving not more than 5-6 hours per day and staying at more interesting places for a day or two. Would 3 weeks be enough or should we go for 4 weeks?
Being European I had no idea that you have to reserve campsites so far in advance to places like Yosemite. Can we still find motels/camp sites near by or is it not realistic at all?


I would appreciate any feedback or any suggestion :) I want to make this trip memorable for my family ...and honestly, I just can't wait :)


thanx

barb