Don't take them to Parrott Mountain, they will be charged and if I remember right its the same as adult price. Although its nice I don't recommend anyone taking young children there. A few years ago we took our grand daughters (ages 3 & 5) to this and to the Titanic. They were bored with the Titanic within 10 minutes of arriving (so don't recommend taking them here either) So we rushed through it and on to parrot Mtn. only to realize after paying it cost us more for this attraction than what it did for the Titanic! Reason was, we had to pay for the girls. So I don't recommend either one of these with young children.
Last Oct. we took them and the oldest one to Dollywood, this time they were 10, 6 & 5 and I believe we had to pay childs price for all three. The younger two were not able to ride all the rides due to height, they were able to ride majority of the rides in the section called "County Fair" and a few big rides with an adult (antique cars, bumper cars, ferris wheel, one roller coaster that stayed inside -Blazzin Furry or something like that, train and a water ride)
The National Park is free. I do recommend stopping at the Sugarlands visitor Center. Maybe the Laurel Falls hike/trail. It is paved but also going up hill but I think its a little over a mile or so round trip. Arrive early, parking lot for this trail is very limited and its a favorite by several. I don't recommend playing in the water at the falls or on the wet rocks. I live in TN. and hear/see to many people getting injuried by negligence around waterfalls and/or mtn. streams. If they like to car ride, take in: Cades Cove - 11 mile one-way loop road and you will be able to get out and explore the old buildings, etc. and theres a visitors center here they may like, has an old flour mill here (still working) among other old buildings. At the end/or near the end is a horse stables, they do offer carraige rides that they may enjoy. Roaring Forks Motor Trail, located a short distance from red light #8 in Gatlinburg, similar to Cades Cove but much shorter and not as congested, great views of Gatlinburg! Clingmans Dome, tallest peak in TN. paved walkway to the tower but another very popular area so depending on the day/time you may have a hard time finding a parking space.