While in Nashville my wife and I hope to visit both DollyWood and Graceland (~3 hours drive away in opposite directions). Are we nuts?
Are there likely to be tours from the hotel or buses there and back? Is it more of a stay-overnight thing, rather a do-in-one-day? Is there a lot to see at each location? Or are they avoid-at-all-cost locations? We’re not Dolly Parton and Elvis fans per se, but thought it might be fun.
Also, is anyone else considering seeing them after XDC too?
Possibly but unlikely because of the visits you plan 
Both are worth a visit but if you had to pick one I would go to Graceland first
Get a rental car and have a good drive.
In Denver I used the chance for some trips to the Rockies and one to Mount Rushmore.
Use first day after arrival when you wake up early to do along drive and leave city before rush hour.
There are several day trips to Graceland from Nashville, this one includes hotel pickup, round trip transportation and the tour. I suggest contacting the Sheraton to see if they have recommendations, since it’s a popular conference hotel they probably know all of the best tours.
Being from East Tennessee, I’ve never been a huge fan of Dollywood. If I had to choose I’d go with Graceland.
That said, the Sevierville/Gatlinburg area is very nice and my wife and I rent a cabin in the area once every five years or so just for the peace and beauty. There’s also no shortage of other attractions in the area. I used to be the IT Manager for one of the companies that owns and runs huge swathes of Sevierville/Gatlinburg entertainment, so I’ve done and seen most of it from the inside out. Lots of fun things to do.