In New Vegas, the Enclave Power Armor is non-factioned. Anyone can wear it.
As the previous poster said, Arcade Gannon's quest is the key to getting access to the Mojave Enclave Remants (one surviving squad from Navarro, plus their gear). It's really not about you joining The Enclave, its about their last surviving squad joining you.
Getting and keeping Arcade is tricky because he hates Legion, and as you probably know The Enclave hates NCR -- they are mortal enemies. You have to walk a fine line between those.
How I made Arcade happy was I finished The Fort on the east side of the Colorado, then I shot up the Legion camp at Cottonwood Cove after I got back, then Arcade was willing to join with me because I now had a low rep with Legion. There are other ways to lower your Legion rep later on in the main quest, but Cottonwood Cove was just quick and easy for a sniper on the return trip from Caesar's Fort so I got Arcade earlier.
There are some oddities in The Enclave quest and I doubt anything has changed in 1.3.
When I did Independant New Vegas I had to ask The Enclave Remnants to side with the NCR. It's just one of those dialog oddities where you don't have a neutral choice. High (very high) speech helps there. Might have been 90 or 100 it was a long time back.
Also, when I did it Arcade just disappeared after we were all ready for the final battle. He was a no-show at Hoover Dam. But you will get the Power Armor training and the power armor itself before this, so thats not a concern. Mainly I was upset he took off with my Plasma Caster and he would have added a lot of firepower
I don't know if Arcade left because I was going with The House (Arcade doesn't like House) or because of a glitch: I read on wikia about him disappearing near The Remnants Bunker, and that was in fact where I last saw him as we were getting ready to go to the dam. But the rest of the remnants showed up at the dam in their Vertibird and they kicked serious butt.
Well, just my 4 bits added to the previous post