I answered on the 'other' forum.
I wouldn't recommend a 2 and 4 yr old to enjoy the places you're thinking of visiting.... especially in winter. Yes, you could get snow at that time but more importantly, cold and bitter winds. We had plans to stay in NM a winter when we first began full-timing. We were in the southern part and it didn't take long to head over to Arizona.
You might want to consider the Benson area of Arizona along with Tucson. There is Kartchner Caverns which the children would enjoy more than Carlsbad. Lots of beautiful lighting and dripping sounds from the constantly growing formations. Carlsbad is nothing like that. There are many places to ride in that area. The days are pleasant but it will be cold at night but not as bitter as NM. Kartchner State Park is very nice as a base.
Nearby Tucson has so many wonderful things that the children would enjoy and it would be warmer.