Welcome to the RTA Forum!

I think you're on the right track, but there are a few areas where I think you'll need to rethink your plans and approach.

First, what are you planning to do for a vehicle that will fit 8 people, car seats, and luggage? Doing a loop trip, where you start and end in the same place can often save quite a lot of money, but if you need to rent a specialty vehicle, that might be your only option.

Two, you're going to have to significantly rework your travel time estimates. I suspect you are using the estimates of online mapping programs, which are overoptimistic in best case scenarios. When you consider that you'll be traveling with half a dozen kids, your actual driving times are going to be significantly longer.

The biggest place that would come up is Sequoia. You really can't drive from Vegas, see Death Valley, and make it to Sequoia in the same day. That's nearly 500 miles, a fair bit of it on 2 lane and mountain roads. Just drive time alone is going to be close to 10 hours, and that's before seeing Death Valley or accounting for the extra time needed for your large group. Even if you skipped DV, you couldn't do it in anywhere near 6 hours. It's 7-8 hours under good conditions, and again, longer for you considering the size of your family.

Similarly, planning to see a bunch of stuff on your first day seems like you're being pretty optimistic. I mean, I wouldn't plan to do much anything at all on that first day. To get a flight that lands in Phx around 10am, that means it will have to leave Florida around 7am, which means getting to the airport at 5am, which means getting everyone up and out of the house around 3 or 4 am (and that assumes a non-stop flight!) and so while it will probably be around 11 am- noon, by the time you get your bags and car and get on the road, and while getting the road by noon means you'd theoretically have time in the day to stop at places on the way to Sedona, you'll have kids who will have already been traveling for going on 10 hours and starting to feel the effects of jet lag.

So, a few things I would do differently, Go ahead and plan to spend the first night around Sedona, but consider anything you stop at along the way to be an unexpected surprise. If you want to still see things around Sedona, then I would plan for 2 nights at the Grand Canyon.

I would do Death Valley after Vegas, but I would stop between there and Sequoia - perhaps around Lake Isabella or Bakersfield.

I would skip Joshua Tree. It's a much longer drive than just 5 hours (even google estimates it at more than 6), and it a fair bit out of your way. I would also strongly recommend AGAINST any idea that has you driving through the middle of the night "while your kids sleep." All that's going to do is mean that they'll be wide awake, when you are exhausted, and that's not good for anyone! I will note, if you end up having to drive back to Phoenix to complete the loop, then I might look at doing Joshua Tree between SD and Phx.

If you wanted to add in another National Park, I'd look at Yosemite over Joshua Tree. If you are going to visit 4 National Parks, you will want to by the $80 annual National Parks pass (it might even be cost effective for just 3 parks).