Hi Danelle,
With the ages of your children, my vote is for
Hoop-Dee-Doo Musical Revue. I think the entertainment, corny jokes, and great food will likely appeal more to your family. Mickey's Backyard BBQ is a good choice for little ones to burn off steam, but for older kids, I happen to think you'll see more value in the Hoop-Dee-Doo. And let's not forget Hoop-Dee-Doo offers air-conditioning, whereas Mickey's Backyard BBQ is held in an open air pavilion. Think ... Florida heat!
I think the biggest draw to Hoop-Dee-Doo is the mere history of the show, dating back to the 70's. It's one of the longest running musicals, having entertained tens of thousands of guests. It's a classic, and should certainly be experienced by any Disney fan at least once in their travels. You often hear of families creating a tradition to attend Hoop-Dee-Doo with their children or grandchildren, as it becomes almost a staple in a child's visit to Walt Disney World. Who knows... perhaps your children will remember your time at the show, and will someday wish to take their children to experience the same nostalgia.
Be sure to book Advanced Dining Reservations by clicking the link above or by calling 407-WDW-DINE.
I wish you luck in your planning, Danelle, and have a MAGICAL vacation!
Sherri