I would think it is far more likely that Junior would pick up brattish behaviour from his mother rather than his father. Katie doesnt regulate her behaviour for anyone least likely her children who hear her berate everyone in earshot.
SInce DOTY is the one who continuously tells Junior he's a star, a chip off the old block, and has him performing for the cameras every week, I can't see how you can possibly point the finger at KP on this one? And surely if it were KP encouraging this 'bratiness', wouldn't DOTY be trying to correct it on his DOTY show - what with him being a DOTY an' all - so he could look all pious and make that long-suffering face he does... and then have GemmaMouthpiece tell us sanctimoniously how Pete is worried that Junior is acting up because of... well, you know... and becoming too fond of the spotlight... Oh wait!! He can't say that, can he! Cos he's the one putting Junior in the spotlight.
How strange and odd that people are so reluctant to call a spade a spade where DOTY is concerned.