I definitely get not going to places you have already been to, when there are so many places see that you haven't.
Two nights in Sedona sounds good, 460 miles from SD is doable.
400 miles to Santa Fe is also doable.
Some areas of interest between Sedona and Santa Fe include, Sunset Crater Volcano, Wupatki Ruins, Meteor Crater.
Normally I recommend Santa Fe more highly than Albuquerque for first time visitors, but one night in the Old Town area of ABQ would make for a shorter day if they spend a lot of time stopping along I-40.
The drive from ABQ to SAF is an hour on the freeway or slightly longer on the Turquoise Trail going through the ghost towns of Madrid and Cerrillos.
I usually recommend at least 3 nights in Santa Fe for exploring the city and nearby areas such as Bandelier, Los Alamos, Valles Caldera, Taos, Chimayo, Abiquiu, etc...
300 miles to Carlsbad should be a fairly easy day. Roswell makes a good, mid-trip break. If your parents are into this sort of thing, they may like the somewhat goofy exhibits at Alien Zone, a few storefronts down from the UFO museum.
Carlsbad Caverns has two lodging choices: the town of Carlsbad and White's City. Carlsbad doesn't have a lot of amenities, but definitely more than White's City, but White's City is much closer and the one motel there is perfectly adequate for most people.
White Sands is really too far away from Carlsbad to visit the same day as the Caverns. The best times to visit the dunes are near sunrise and sunset. I would plan on staying overnight in nearby Alamogordo,
From Alamogordo, 750 miles is probably too far to make it back to SD in one day. The midpoint would be somewhere near Tucson AZ. So you are still looking at 10 nights. Modified route:
https://goo.gl/maps/xeBhTdagGgYAkdfk6
0 San Diego
1 Sedona
2 Sedona
3 Albuquerque Old Town
4 Santa Fe
5 Santa Fe
6 Santa Fe
7 White's City/Carlsbad
8 White's City/Carlsbad
9 Alamogordo
10 Tucson?
11 SD