Not following exactly what you're saying. Are you saying you have a full Service load calculation which covers all the equipment in the house (and square footage, kitchen/laundry appliance circuits, etc) and the pool equipment? If so, that's the first step. Next, is there a feeder to the pool area which will be running just the pool equipment? If so, perhaps this is the load calculation he wants. If not, perhaps just take your Service load calc and highlight the pool equipment (either just the new permitted stuff or new and existing).
His permit may be priced by branch circuit or feeder size in amps. But I don't know your role -vs- the pool guy's role, what is being changed, and who is buying permits for what.