Hello and welcome to the RTA forums !

I'm also looking up stuff on other peoples threads for ideas. Thanks!
It's good to look around the forums for ideas and find things that appeal to you, but untill you have decided on your route it's impossible to give any useful suggestions. As you look around you will find one common reply "there is no best" as everyones tastes are different and each journey offers fantastic places to visit so the 4 of you are going to have to sit down and make that decision before we can be of much use.
At this stage I will point out that I think you might be underestimating how long going to New Mexico will add to your trip. If Carlsbad caverns were in your thoughts the trip would be over 2800 miles and the majority of your waking hours will be spent driving. Of course there are still many great parks to see in Utah and Colorado without the need to go to NM.