"So....being of sound mind (she is) and if we were to use extreme caution, would we be foolish to give Mount Rainier a try? "

Yes.

Rainier is a very different animal. It is not just that you are on slopes as/more severe than the chute for a couple of days straight, it is that the terrain that you are travelling over is far more dangerous.

On Whitney, it is pretty hard to get lost. On Rainier, you are on wide, exposed areas all the time, with little to orient on. Throw in a little whiteout, and it becomes grim.

You absolutely need to know snow travel skills. You need to know how to climb on snow with ropes. You need to understand, have practiced, and be skillful in crevasse rescue and rope management, which is much harder with only two people. Usually you want three on a team. Two would be for two experts.

You need to know how to read the snow, both for crevasses, and avalanche danger. You need avalanche transceivers, and have trained and be quite practiced in their use. You need to do all that on snow.

You need to have high-quality gear, not the stuff "you can get away with" on Whitney.

"Exteme caution" reveals what you are lacking. There are places on the route, where you are in serious danger of snow/ice falling on you from far above. You need to know how to recognize them. But when there, "speed=safety". You get your ass across those spots FAST. Good weather may actually be the more dangerous time, as things melt and fall.

If you don't already have it, Mount Rainier: A Climbing Guide, by my friend, Mike Gauthier, former chief climbing ranger, and founder of the climbing ranger program, is must reading.

Also, take a look at his site: http://www.crevasse.com/

Here is the ranger blog:
http://mountrainierclimbing.blogspot.com/

Also good to give perspective:

The Challenge of Rainier: A Record of the Explorations and Ascents, Triumphs and Tragedies, on the Northwest's Greatest Mountain by Dee Molenaar

The local climbing board for Rainier is
www.cascadeclimbers.com

Rainer is a great mountain to aim for, but it is a serious place that deserves serious preparation, education, and training.

G'luck!