1) If you Wikipedia the two bikes specifications you see the DR is more powerful @ 15hp & 17.7 ft.lbs. torque. Both seats are reasonably low. A few specs differ here and there ( like tires) but those are just numbers. I would say the major difference is in the feel and intended use of the owner. Want to comfortably commute at speed, learn to wheelie, ride more street than dirt? You might prefer the DR. Want to go trail riding with your daughter as you two explore Arizona? Then I would really recommend the TW. You could youtube both bikes and see how others ride theirs and see what suits your style.
2) There are lighter options that would be easier but YES the TW200 would be a good starter bike.
3) Not from AZ but I imagine cost is a function of model, engine displacement and your Zip Code. Internet can give accurate quotes.
Jim, you sound like a perfect candidate for a TW200 as long as you do not have extensive freeway expectations. The TW is a lot of fun on surface streets. Off-road it is quite enough, and torquey enough to put-put alongside your daughter and talk back and forth. Should you lead ahead your comfortable speed might better match hers due to low trail friendly first gear.