I'm sorry, but I think you're going to have your family pretty burned out and miserable by the end of the first day.

Put it this way, you're going to be getting up at 1 am Vegas time, and plan to be on the go non-stop all the way until sundown! You really think your family will be in any position to have any fun by the time you get to Zion at that pace, much less be in any mode to race on to Bryce the next morning?

I wouldn't even try to see Zion on the day you arrive, as Valley of Fire, along with 2-3 hours of driving to Springdale, plus a near coast to coast flight will be more than a full day already. See Zion the following morning, and head onto Bryce as Dave suggested above.