A couple things:
A motorcycle safety course is a great idea. It may seem a little slow paced but they really do drill the basics into your head with heavy focus on slow speed maneuvering. Being able to navigate your bike at 2MPH through a parking lot comfortably is just as important as being able to rail through the canyons or blast down the dirt roads. As you're both all too aware you can just as easily injure yourself in a parking lot as you can out exploring the wilds.
Too heavy, too tall and in denial. You said you laughed at the suggestion she try a lighter bike like a Ninja 250. While the Ninja is technically similar in weight it is also a much lower bike that carries it's weight down low. The DR is a tall bike that carries much of it's weight up high. If you sit on both and try walking them around a parking lot and putting a foot down at a light you will realize that even though it's curb weight is similar the little Ninja will feel like riding a mountain bike in comparison to the DR.
I mean no offense with my comments. I made the same mistakes, my first bike was an 08 KLR650. I am 6'1" and 200lbs. If I could go back in time I would punch myself in the face and buy a little 250 dual sport instead. Can your girl squat 350lbs comfortably several times a day when she's already worn out from riding and probably a bit banged up from dropping her bike? I know it took about 2-3 times picking up my KLR before I was hating the day and wishing I was doing just about anything else but riding...
Park the DR, get her a little 250 to learn on and hop back on the DR once she's comfortable. You will both be MUCH happier in the long run.
2008 - KLR685 - Currently For Sale
2008 CRF250x - Street Legal Hooligan Machine