When, in November?
Realize that Santa Fe can get quite cold, particularly in the later part of November, and does get quite a bit of snow (for the desert). It may be better to stay south. I just assume, coming from Montreal in winter, that you'll not want cold or snow.
Also, how long would you like to drive each day? White Sands to Santa Fe will take you about 4 hours, as will Tucson to El Paso, and that's non-stop.
You can do some light hiking at Guadalupe Mountains National Park, but you will not be able to make the peak round-trip in 4 hours. It's a tough hike anyway. Lots of hiking at Big Bend though (one of my favorite parks) of all varying degrees and lengths.
Have you already booked the Chisos Lodge? I ask because it can get very crowded and books up very early in the spring and fall. It's the only in-park lodging in Big Bend, so it's very popular. That would be a good start, and then plan from there. I think it would be best to hit Big Bend first, unless you plan on going to Santa Fe, then it would be best to go there first. Just to be able to beat the weather.
One specific recommendation I would make, if you do go to Tucson, is to come back via Columbus on Highway 9. It'll add, at the least, a half hour, but it follows the old passenger railroad route from Bisbee to El Paso, and it's a very interesting and scenic drive. Columbus is also an interesting enough town, with its Pancho Villa folklore. And that's an easy place to cross the border, though I don't know that I would do that right now.