Mr. Miller,
Congratulations on having two homes. However, no matter how you cut or dice it, only one home can be your primary resident. However, for the appraisal I would mark it either owner occupied, tenant, vacant, and explain what I observed at the time of the inspection in the addendum.
Why is it that so many lenders will not finance a second and/or vacation home even if they are by your definition "owner occupied"? Try getting FHA financing on your second "owner occupied" home.
As far as Primary resident is concerned it can be identified by: which address do you use to vote in the general election. What address is on your driver's license? Where is your car registered. Which State Tax do you pay income tax? Which home do you claim and deduct on your federal and state for the mortgage interest?