Dog Canyon, worth it if not camping?

We're planning on spending a few days in Guadalupe Mountains NP this upcoming May. We won't be camping but rather making day trips from our motel in White's City. Is it worth making the drive from White's City to Dog Canyon? We would probably do a bit of hiking and just view the scenery.

If we do decide to go, is the road possible to drive in a regular passenger vehicle (mini-van, to be exact)? Which route would be the fastest from White's City? I see on the park map a road that I think is dirt/gravel just a bit north of White's city that leads across to the road going into Dog Canyon. Would this road be safe to take, or should we drive into Carlsbad and take the road from there?