This guy was pulling a 35' TT with his Armada until he traded for a F-350 diesel.
BUT his trailer was a lot longer and heavier (8500# dry), and he says the Armada did a respectable job towing it, but he traded because he was down to his last ounce of ratings. So with your size/weight TT you might be OK with the Armada.
Of course that means installing a brake controller in the Armada, getting proper mirrors, etc....
If this is the first time taking DD and the kids, maybe worth going somewhere close to home where they can follow easily in the Armada and see how the family camping thing works out with the TT before investing in tow gear for the Armada.