Re: 220v electric sub panel schematic help
It is not clear (at least to me

) from your diagram how the 6/3 cable is connected at the two panels.
At main, the red and black go to the 60 A. breaker and the white to the neutral bus.
At sub, it should not go to any breakers. (unless there is a main breaker, which I would doubt.) Red and black terminate at line buses, white to neutral bus.
Check codes in your jurisdiction, but irrespective of their minimum, I'd suggest a disconnect before both the sub panel and the hot tub. (obviously if your sub-panel has a main breaker you don't need a dx)