My 2013 Armada Platinum has a 9,000 pound tow rating with the optional tow package. I believe the easiest way to determine if you have the tow package is the tow package includes the transmission temp gauge. They have a lower tow rating without the tow package.
If you log into www.clubarmada.com
(Towing Section) you'll find a lot of Armada/Titan owners who know a lot about towing with these vehicles. Biggest problem I had was getting the hitch set up without getting interference from the auto-level system on the Armada.
My Armada (for those who don't know, the Armada and Titan are the same vehicle except for the body style) tows my 22FB with no problems at all. I always tow in 4th to keep the transmission from locking/unlocking and shifting 4-5-4 all the time.
Nobody has ever been able to tell me exactly what the tow haul mode button does. Everybody says it changes the shift points but nobody knows anything specific and I haven't been able to tell one bit of difference. I think all the button does is turn on the light.