I love my privacy and my kids' but I don't understand this extreme behavior... She is worried that companies know she has kids? Can't they just pull public records to see that? Or read this article published under her full name with attached social media profiles?
Personally I don't want to be tracked by Disney in the real world, but wouldn't mind it inside the park. Or, like another commenter pointed, just don't go. Disney will track you with or without a band (isn't every square inch of the place under CCTV?)