I suggest that you take a look at the area on Google Earth. NM-14 is a good two lane road and a scenic drive. We have driven it pulling the trailer a number of times, but never try to stop.
There is very limited parking in Madrid. It may be possible to park a large rig on the side of the road if you can find a long enough space between other vehicles. There is a space at the top of the hill on the North end of town that can accommodate a large motorhome or two. I've never driven down any of the side streets in town so no idea what may or may not be available for parking on them. The last time we were in Cerrilos, there wasn't much of anything open.