I have taken both of my niece's to HDDR, they were almost 6 and 4.5 yrs when they went.
The 4.5 yr old was laughing and seemed to get the jokes. Her older sister had the worst seat at our table and had her back to the show. She still seemed to have fun.
I haven't been to the Backyard BBQ, but I have heard that it's kind of a free for all with the characters. It's outside so depending on when you are going it could be quite warm out.