Weighing in late here, but fwiw: Our family of six did a 7000 mile cross country trip very comfortably in our '01 PSD Excursion. I upgraded the sway bars, shocks, added air bags, and loaded a software upgrade (set on tow). I should have upgraded the springs, but the dw was opposed to stiffening up the ride.
I destroyed two transmissions in two different mountain ranges (one before the big trip and one during) before I realized that the software upgrade (even in the lowest "tow" setting) will help the already powerful 7.3l engine overheat the transmission. In short, just because it will climb at 70mph, in overdrive, doesn't mean it should! Expensive lesson learned:) If you go this route, install a tranny temp gauge.
I agree that one of the duramax powered vans may be a nice alternative, however our tow vehicle is my wife's daily driver and she refused to have a van.
Depending on the ages of your children and the distances you plan to travel, having space for and access to a porta pottie in the back may find its way onto your list of considerations.
Enjoy your travels with your family!