The PC must challenge Bares-His-Teeth for leadership of the group by pitting his dog against the Packleader's dog. It's not likely that the PC can succeed unless he has the Devil Dog on his side, but there may be alternate methods.
Science Boy - Develop steroids to use on his dog before the fight so he wins. Or metal teeth.
DiploBoy - Talk to the Daughter of Hecate into helping him. Maybe have the Daughter declare Bares-His-Teeth unfit as a leader and threaten a fertility curse if the PC isn't made the new leader immediately?
Stealth Boy - Slip a soporific into the dogfood, making the Packleader's champion sluggish and more easily defeated.