GFCI circuit for hot tub tripping after move

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.

There are essentially two possible reasons:

1. There is a ground fault in the wiring/fixtures/appliances it's protecting
2. The GFCI itself is faulty

It really depends on what's on the circuit to determine if there is a fault somewhere. 15 year old wiring is likely to not be a huge issue. There could be water in a junction box. Simple receptacles and switches aren't too likely to have issues (though it wouldn't hurt to open them to take a look at the connections), but anything with active electronics in it (dimmers, USB chargers, etc) could definitely be the cause. Same goes for other fixtures -- lights, ceiling fans, etc.

You could replace the GFCI and see if it still happens -- if so, there's definitely a fault. If you don't have another GFCI already, this is a somewhat expensive way to test (though if it's fault, you'll have to buy one anyway).

If you happen to have another one you could swap in, that would be a cheap and easy way to test. Swap two, see if it still trips and if the same breaker trips, or the same circuit trips the new breaker.