I'd personally argue and say he didn't care so much about Pucci as he did about achieving his own goals and furthering his personal ambitions. Pucci felt more like a malleable pawn.
If we're going by the overheaven novel, he respected his father more than his mother iirc.
Pucci is the only one on here that actually allows DIO to reach his goals and I don't think it takes much to argue that DIO would choose his goals over his own blood any day.
Its the idea that someone who reaches their goal attains true heaven. Like I said earlier, if were going by the overheaven novel, DIO truly believes his father went to heaven while his mother burns in hell.
