I think it is a little bit of both sides that caused the problems. The dad is a loud mouth but so are the kids. Paul Jr. is talented but also lazy at times and Sr. always went out of his way to prove he didn't give Jr. special treatment but went too far. Sr. probably needs to relax a bit and not be so hard on his son but Jr. needs to work hard and show everyone he is not above the rules. He would come and go as he pleased which is never good for your employees to see coming from the boss's son.
The problems only got worse when Jr. left since he had a 20 percent stake in the company. There were issues over his buyout based on when he left. Jr. and Sr. argue over different dates of departure which affects the buyout and Sr. claiming the company is worth zero which brought on the "let me buy your 80 percent then" comment. It's never good for a father and son to end up in court over a financial dispute. Then again, it's a TV show so who knows how their relationship really is.