I noticed this last year, but Pixar's films (intentionally or not) can all be related to something that educates parents into being better parents. You can probably read something different to me for each film, but I think this might have some connection to why they are such good family films.
Toy Story
Kids give toys personalities and this can show you how they relate to other kids.
Toy Story2
Toys getting dirty is ok because at least they are played with.
Monsters Inc
Kids sometimes need to meet the monsters in their closet to overcome the fear of them.
Finding Nemo
Being too controlling as a parent is wrong.
Incredibles
Let your kids be who they are so they can shine as individuals.
Obviously everybody loves the characters from all the films, but kids and adults love different plot ideas and this is what makes targeting a family film difficult. Kids can't cope with complicated plots and don't like Drama or Romance films, but Parents don't want to be watching The Brave Little Toaster again either because they where subjected to these kinds of stories when they where kids and they have developed past that.
What Pixar seems to do is it to find somekind of middle ground that both adults and kids can relate to. You can analyse that yourself, but I think this kind of design idea will have big implications to games in the future for targeting difficult markets.