Dove Mountain is REALLY out of the way, good if you want to stay at the resort mostly, bad for general sightseeing.
Kartchner Caverns is very far southeast, so even rush hour traffic shouldn't be much trouble. From La Paloma, I would head east to Swan Road. South on Swan to Speedway, east to Houghton Road, then Houghton to I-10 and east from there.
I have taken the Rotunda/Throne Room tour probably at least 6 times and the big room tour twice. I much prefer the Rotunda/Throne Room tour. If you get an early enough start, you can also see Tombstone and Bisbee on the same day, or Sonoita / Elgin wine tasting.
Also, during the Summer, a day (or at least an afternoon) on Mt. Lemmon is mighty refreshing -- 30 degrees cooler than in the valley. Do that during the week to avoid horrendous crowds.
Edited: 7:09 pm, March 03, 2013