Eddie,
I'm having a hard time making out what you're trying to say in BOTH your posts here, so I may be off in my response...
I noticed you other post in the general (non-state-specific) "Open Carry Questions" area, but couldn't answer you as I'm not well versed enough on the laws (NM or TX) to answer that for you...and also you were asking about driving back & forth from TX to NM -- so that'd be questioning 2 state's laws.
So, I was going to suggest your post your question here in the NM area, and maybe even the TX area.
I used to live in El Paso (for a LONG time), and often went up to Las Cruces (usually cruising up to "Cruces" the back way (Hwy 28) on my big V-twin MC), so I also had to think about how/where I could or could not carry. But I never went to the Las Cruces Mall -- I assume you mean the Mesilla Valley Mall (MVM) -- while carrying (either CC or OC) so I couldn't tell you anything. Also, I left the El Paso in 2008 so I don't know any signs the MVM may or may not have since then or NOW. Heck, I never even got to go to the Cattle Baron steakhouse near the mall (up on Telshor). I'd also go to the Village Inn often (Lohman & Telshor) but wasn't carrying at that time (long story). My only RECENT experience OCing in NM is in the Rio Rancho/ABQ areas when I OCed regularly...but I never went to any malls THERE carrying, either. TMK, OCing (at least) -- like at Cottonwood Mall in ABQ -- is not allowed. Frankly, I don't know ANY mall that allows it, signs up sayin' so or not. In any state! Consequently, I would err on the side of caution and NOT OC in ANY mall in NM...
TMK, in TX you can have a handgun (or long guns, loaded even) in your car (no permit needed) as long as it's covered (concealed) when/if a cop stops you (he's not supposed to be able to SEE it as he looks in so just cover it up with something temporarily when/if you get stopped). When you get to NM, you can put it on your belt (OC, no permit required) or have it out and NOT hidden (IIRC) from view, since being in your car is considered like being in your house. CC requires a permit in both TX and NM, but a TX permit is recognized by NM and vice-versa.
No, you do not need to be a RESIDENT of NM to OC...simply being IN that state allows you to OC without a permit -- where legally allowed, of course (AND where you don't see any "No Guns Allowed" signs posted at some business/restaurant). When on my MC going to Las Cruces, upon reaching the TX/NM border I would pullover and went to OCing my handgun. Of course, when returning to TX, I had to do the reverse! Up in th RR/ABQ area, I'd OCed in Starbucks, Home Depot, a locksmith shop, Village Inn, and a pizza place. No problems anywhere. I would think that Starbucks, Village Inns and Home Depot in Las Cruces would be no different. But it's always good -- just as a prudent habit to develop -- to check for any signs posted at the doors, especially at one-off Mom & Pop places that may be posted.
I'm sure a NM resident will come along soon here and help you out.
And as I said, you may want to post over in the TX area for TX-specific questions and wait for someone more knowledgable to respond.
While waiting, you might want to look at some older threads here in the NM area and search for members who indicate they live in Las Cruces...and then perhaps PM him directly (if no one else can help you). If he is still around and checking this forum occasionally, he should see the PM and get back to you.
Good luck...