Peter is brutal and cruel.He believes in "strong emotions and weak emotions" and thus is a regular jerk. He has a superiority complex and thus believes that he should have been Preston Hagen's favourite grandson.
He has a cruel sense of humour and can't help but 'sign his name.' An sample of this is that he owns a fake but real looking gun that has a flag come out it when the trigger is pulled. On the flag, instead of the word "BANG!" on it it has his full name on it.
Peter has a lack of morals. While Basil won't hit a member of his family, Peter has no problems with this: having hit Basil over the back of the head with Basil's own ukulele also showing Peter to be something of a coward.