OP, the Tundra with the 5.7 has tons of power. You won't be disappointed with the engine or transmission, that's for sure. Like others said though, the limiting factor on a half ton is the low payload. You and your wife, kids, a big dog, firewood... that adds up to a lot of weight. I would guess you will be over payload on a Tundra. The engine is up to the task... but everything else isn't as stout as a 3/4 ton.
I just traded my Tundra on a Ram 2500 last week. I was over my payload with everything we bring camping now. The 3/4 ton Ram should be a better match with my heavier trailer and all the gear we bring with us now.
Do yourself a favor and look at the 3/4 ton offerings. My FIL tows with a Chevy 6.0 and has no complaints. The Ford 6.2 is a proven engine. The Ram 5.7 is proven, and the new 6.4 looks to be a very nice option as well. Any one of those trucks will tow your rig just fine. Expect 9-11 mpgs AT BEST with a gas engine, a couple worse if you are in hilly terrain.
Put your family in a couple trucks, find one that is comfortable for you. Make sure you get at least a 30 gallon gas tank too... those trucks are thirsty!