Oh, now that there are plans in place for his death you’re calling him cousin? He’s family now that he’s got a death sentence hanging over him?
And he’s not calling him family in that creepy stepdad way of calling him son. Cousin is actually accurate in the sense that it was used then. It’s family. It’s relative. It’s familial and familiar. Unlike calling him “son” – it is not combative. Claudius is finally learning how to be a better stepdad moments before he’s due to lose the job.