Electrical – Hot tub wiring extending existing wire

Regardless of what all the individual breakers add up to, the maximum you can draw through that subpanel is 60amps. Realistically you want to be a bit lower then that to allow for some spikes.

To determine if you can support the tub, you need to take a measurement of the current (amps) on the circuit with some or all of the existing devices in use (i.e. normal use). Ideally you would use a clamp meter around the hot wires in order to measure this, but alternatively you could add up the loads on the circuit. If you subtract this value from 60, and you have enough capacity for the tub, then it should be OK to run from that sub-panel.

If the two circuits are wired with 14-2, all you need to do is identify which neutral goes with which circuit and disconnect them from each other, so each is only connected to the items on its circuit.

This would only be a problem if the two circuits were actually sharing a neutral wire. If they simply have joined neutrals, it's easy to remedy.