Pigeon Forge and G'burg are in my backyard! Come on down...we'd love to have you visit the area!
Many great ideas have already been given so I don't know if I can add much more. If you are coming this summer & plan on visiting Dollywood, Kidfest begins June 17 and goes through August 7. There are special shows and activities planned to appeal to children. You can read more about it here -
http://www.dollywood.com/KidsFest.asp
Dollywood also has an area of the park designed just for kids. It's called Imagination Station and can keep kids entertained for a while so parents can sit and take a break.
Traffic is definitely a bear during the summer. Take the trolley when you can or use the backroads as much as possible. If you decide to attend one of the music shows, be sure to allow plenty of time to get through traffic to arrive at the theater or you will miss the start of the show. I highly recommend the Louise Mandrell Show. She always puts on an excellent performance.
This site has a lot of info and if you click on Calendar of Events you can see what's going on in the area in the upcoming months -
http://www.pigeonforge.com/index.shtml
Take Hwy. 441 over the mountain into Cherokee, NC and there is a great show called 'Unto These Hills'. It's performed by a cast of Cherokee Indians in an outdoor theater and depicts the trek they were forced to take (known as The Trail of Tears) when banished from their land to Oklahoma. It's a very moving play. It gets cold in the mountains at night so, if you go, take jackets to put on as night descends. We have even taken blankets as well. It's 21 miles over the mountain to Cherokee but they are 'mountain miles' so be prepared for twists, turns, & heights!
As you are coming into the area on Hwy 66, you will see a large building on the right called Smoky Mountain Knife Works. Someone has already mentioned this and there is a lot more to see in there than knives, altho' there are many of them & they are quite interesting. Nearby is a huge store called Home Accents Direct. I love going there and always find really unusual items. There is a camping store inside for the guys to browse and a Black and Decker outlet store is also across the street. Gotta keep the men happy while the ladies shop!
If you come at the right time in June, the mountain laurel and rhododendrons will be blooming and they are beautiful. There are thickets of them all along many of the popular mountain drives.
I just found this thread so I'll think some more & see if I can come up with more ideas.