Way too much driving. Pick a couple of major parks and spend a week or so exploring them. I have to agree on Houston not much to see there.
As for the heat as a fellow Floridian. It's different the humidity is a lot lower and it won't feel as hot as it really is. But you will dehydrate rapidly, make sure you always carry plenty of water with you. At least a liter each when you go on hikes. And use sun block. We usually try to do our hiking early in the day before 10 AM.
You are also driving past some major parks, Carlsbad Caverns for example really is a must see. White Sands NM is worth at least a drive thru and so on.
Concentrate on one area, the Four Corners loop for example. Take your time and enjoy what you are visiting. I have to admit you did make me laugh with the question: "Is one day enough for Yosemite?" Over the years we've spent several months there and I'd go back tomorrow given the opportunity. They'll be other trips so don't try to do it all in on fell swoop.