Looking for Loopholes
The fight between Junior and Senior didn't end in that explosive argument but what followed the feud is that Senior looked for possible loopholes in their contract that would allow him to buy his son out of the company.
The Million Dollar Lawsuit
Senior found a loophole in their contract and tried to exploit it by forcing Junior into selling his shares in the company. When Paulie refused to sell his shares, Senior sued his son for a million dollars, thinking Paulie would back off and settle out of court but instead, Junior doubled down and hired his legal team, and Senior ended up losing the lawsuit.