How do I switch iTunes accounts on my iPhone?

That’s the way it’s meant to work. The iPhone uses the account that was last used to access the store from the computer with which it’s synchronized. Try logging your dad out, logging in, browsing the store, restarting iTunes and synching. You may have done all that already, in which case I’d send an email to Apple support, or pop into an Apple Store if that’s an option. Hope you solve it.