I don't understand how Jonathon is supposed to have inherited Joseph's stuff.
Didn't Erina take on that dead lady's kid as per Josephs request? That would mean Jonathan isn't biological.
The baby which grew to be Lisa Lisa married Erina's son George Joestar II and together they made Joseph. Also you got the order the wrong way around, Jonathan is the Joestar which fought Dio in part one, and Joseph is the Joestar which fought the pillar men in part two.
No George II the Joestar which could not use the ripple