Dollywood can be easily done in a day. The only section that you *might* not get to ride everything would be the County Fair section, which is a lot like the Grand Expo. Do be aware that Dollywood DOES charge for parking unlike Silver Dollar City.
As far as Gatlinburg/Pigeon Forge/Sevierville. There are a lot of "touristy" things that are fun to do. My personal favorite is Ober Gatlinburg. This includes a large ski lift up from the strip $11 round trip. Then up at the top you can find lots of activities, kiddie rides, ice skating, a maze OR my favorite, another ski lift up to the top of the mountain. You can either get a POP wristband and do everything OR you can buy tickets for different activities. It is $7 to do the slide, which is a must do. You ride on a small cart down a trough much like a toboggan. Lots of fun.
Other fun things to do in Gatlinburg include the Aquarium of the Smokies. One of the best around. There is also Ripley's Believe it or Not, Guiness Book of World Records and lots of other fun things to do. Hillybilly Golf is my pick for putt putt in the area. You ride an elevated train up the side of a mini-mountain and then work your way back down the hill as you golf. There is also another ski lift that is like $16 that takes you up another mountain, the catch here is how steep of a grade the lift is. Not too bad going up, coming down is another story.
The Nat'l Park is about 12 miles from the south part of Gatlinburg. Honestly, if you do any of the lifts, you see about as much as you'd see in the park itself. Not saying it is not worth going, but in all honesty, unless you HAVE to be in the actual park to claim the credit of being in the Smokies... save your time and just do a lift.
Hope this helps. Oh -- the major "back road" to stay off the main route through town in Pigeon Forge is Veteran's Blvd. Think of it is as the "Yellow Route" to Dollywood. It connects at the north end of Pigeon Forge and then goes all the way to Dollywood and out at the south end of PF. Use it whenever possible as the main highway is terrible. (think 76 with 4 lanes)