As you state your trip plans, I'd say that's a difficult itinerary (not QUITE impossible to travel like that, but impossible to see much), but I'd agree with Isaac that you should do one or the other unless you fly to one, rent an RV, then round trip to/from the other, then fly home.
Driving from FLA to NM/AZ, seeing the sights, then returning home is fine in 4 weeks, allowing a MINIMUM of 4 days to get there, preferably adding a couple more to minimize fatigue and let you enjoy your trip better. Taking the same (or more) time to get back home, still leaves time to see a few things.
Distances are long out there between sights, with very long areas of (as some might say) miles and miles and miles of nothing but miles and miles and miles, though to my taste, most of that western country is gorgeous, but it is decidedly different from what most are used to. Add in that RV travel is more tiring, mile for mile, than car travel and there is more "life maintenance," that is, setting up camp, hooking up to facilities, getting things in the RV from travel to living mode (slides out, leveling, etc.), then cleanup in the morning, followed by breaking camp (put stuff away, pull in slides, retract levelers, unhook, etc.).
AND, if there are kids along, other considerations apply, including letting them enjoy the trip by not keeping them cooped up in the RV on the road for 12+ hours a day.