Quite often kitchen exhaust make-up air is unconditioned, and for energy reasons needs to remain unconditioned. By using a short circuit hood you would make up 60-80% of exhaust. In very cold climates you might want to temper the make-up air.
You might also want to factor in the required...
If this is an indoor pool, or Natatorium, you will want to update yourself on design issues discussed in ASHRAE HVAC Applications (1999 or 2003).
Poolpak
Dry-o-tron
Decktron
are all pool equipment suppliers with design info.
Conditioning pool enclosures can be tricky. Approach with caution...
Homeowner DEF doesn't have a leg to stand on, unless there is more to this story than has already been told here. Seems the former homeowner should have more to worry about, if anyone (disclosure).
Anyway, this is really a legal question and should be directed to someone that is farmiliar with...