Erin,
As for
Mickey's Backyard BBQ, it is typically open on Thursdays and Sundays (and occasional Tuesday), and yes, it is open seasonally so it could be closed. But during your visit, it is open on the 14th and 16th.
So I really like it. I do. But I think I would opt for the birthday/anniversary celebration to be held at Chef Mickey's instead. Why?
You sit at park tables where you are with a lot of other people. I love that at places like this and the Biergarten, as it is a great way to meet other families, make new friends, and just have a fun time. But for a family celebration, I am not sure I want to share that way.
I also think that for a 3-year old, it is not the greatest character experience. They don't get table side visits, but instead have to go and dance with them and all the other kids at the meal. When my youngest went there the first time (she was 1 month shy of 3), she got jostled around by other kids, never really got to connect with the characters, and generally did not have a great time. That is not a slam on the experience, she was just too young.
BOTTOM LINE: Stick to Chef Mickey's, where you are the center of attention, Mickey visits you (not the other way around), and you have a memorable family time.
Have a magical (and delicious) vacation!