Oops. Kinda misread the question. That is indeed the case. Everything changes though, not just the family. Story, recruitable characters etc. change as well. Essentially they are seperate games entirely, in alternate universes based on your choice.
I'd go for the special edition if possible. Both games on one cartridge, the third route as well, and some free collector's stuff. (Make sure to get it as soon as it drops though. I barely managed to get mine, and that was pnly a few hours after it did.)
