DRIVE IT!!!
I did the same thing in 2009, but from Los Angelos to Northern Michigan via Rt. 66. It was a fun adventure that I still enjoy reflecting back on.
My wife gave her blesssing.... but I did it alone.
A few tips.
1- Get a AAA membership before you go. They have a couple day requirement before activation so you cannot break down and then join from the side of the road.
2- Bring/buy some simple tools.
3- Do a test run before you leave of 100 or so miles. This lets you know about the cooling system, oil consumption, gas mileage, and allows you to listen for odd sounds before you start trekking across the desert. (Mine had a 3/4 plugged radiator.... glad I did a test run).
4- Enjoy! If everything works out, you have had a fun trip to share memories. If something breaks down, you might have to swallow your pride..... but it will make a good story a few years down the road.