Hi Kim,
You're going to visit Walt Disney World Resort at a great time of year. It is so beautiful with all of the holiday decorations up!
Mickey's Very Merry Christmas Party is a lot of fun. You are going early enough in December that the crowds at the theme parks should not be too heavy. Since you are choosing between a Tuesday and a Thursday, which are both weeknights and therefore should not draw as much of a weekend crowd, I think you could really go with either. I might recommend the Tuesday just because it will be earlier in the trip and you all might have more energy and be able to really enjoy the party late into the night.
I love both Hoop Dee Doo Musical Revue and Mickey's Backyard BBQ. I think that given their ages and that the children are boys, I would choose Hoop Dee Doo Musical Revue. We recently attended Mickey's Backyard BBQ, and it was a lot of fun, but the entertainment includes dancing with the characters, which your boys may have outgrown at this point. They might enjoy the entertainment at Hoop Dee Doo Musical Revue more.
For other must do's - it depends on your specific boys. If they really enjoy Star Wars, be sure to go to Disney's Hollywood Studios where they can ride Star Tours and train to be Jedis at the Jedi Training Academy. If any of them enjoy Phineas and Ferb, try the
Phineas and Ferb Agent P: World Showcase Adventure at Epcot where they can help to foil the evil plans of Dr. Doofenshmirtz in an interactive adventure which takes place around World Showcase.
I hope that this information is helpful for you, Kim. Have a great time planning your Walt Disney World vacation, and please do not hesitate to ask if you have any further questions.