Effy,
Just to help you plan, I have found that we average about 50 mph when travelling. Sometimes a bit more, sometimes a bit less. But with construction, traffic, fuel stops, etc., the 50 mph is usually a good guide (for Interstate & Highway travel). You only want to travel 6 hours per day, so that's about 300 miles per day.
Using those numbers, you have about a 9 day trip to get to California directly, and then another 9 days back. In other words, 2 1/2 weeks just traveling, and that doesn't include a detour to Tampa, which would probably add another 2 days or so.
Two or three months...sure. Two or three weeks? I think you need to reassess your goals and travel plans.
I understand about planning around the summer school vacation schedule. Is this because you or your spouse is a teacher, or because you will be travelling with children? (On edit: Oops, just reread that your 13 y.o. son wil be with you. If he's a video game fiend, than he'll be happy as long as he has games. :) ) With younger children, you'll probably want to take even more frequent breaks along the way, and I'd plan a "down day" every two days to get them out of the RV for a spell. It just makes the entire trip more enjoyable.
I've been trying to plan a similar trip with our family within a 6 week window and it's tough, and we're not including Florida or any East Coast points in the trip. We are a bit further north & east, of course. Recently wifey has been getting time driving the rig and the kids are old enough to be navigators, so we're hoping to be able to spend 12-18 or more hours on the road on some days. That will probably make it doable. But limiting yourself to about 300 miles per day won't even get you through of some states in a day! Not like up north here were we can see 6 states in a 300 mile round trip...almost! LOL :)
Good Luck,
~Rick