J.,
My husband, two kids (two and four) and I are heading to Tennessee this month. We have rented an RV, because we have made the trip by car and it was miserable.
My suggestion is to do simple activities with a three year-old. Our first stop will be in Hot Springs at a KOA (they also have cabins if you don't have an RV). They have a heated pool, put-put and a convenience store with ice cream. We'll probably roast marshmallows and hot dogs and go search for bugs (my sons favorite activity).
Our next stop is at a nice site in Townsend near the entrance of the Smokey Mountain National Park. On our way home we are stopping in at a music festival in Little Rock.
Ok here's my point, I've been to Graceland twice. First time I was 13 and my brother was 10 we were both bored...a three year old will hate it. I've been to Gatlinburg and Pigeon Forge many times...pretty cheesy. Shows are expensive and not worth it for little ones. There is a new aquarium in Gatlinburg and kids may find the taffy shop fun (they make the candy in the store window.) The park is fantastic, but can get busy in the summer. A drive through Cades Cove is nice and you will see many deer and a possible black bear.
Have you thought about Chattanooga? There is a nice aquarium there as well, the Choo-Choo and Rock City.
Write me if you want to know more. My husband is from Knoxville and we lived in Birmingham. We've traveled all over the deep south, so I would be happy to give you more advice.