Are your lenders local? You could ask your loan officer to swing by - also, an idea is to pay an appraiser a small fee to do a walk thru inspection. I'm sure there are plenty who would charge well under the price of 2 separate appraisals for 20 minutes of their time to render an opinion on the level of required repairs to meet the guidelines of the loan you are planning to go with. When I have any question, I'll pay an appraiser I work with and trust for a second set of eyes.
Secondly - if you don't want termite to be a condition, don't include a termite inspection in your sale documents. If it isn't called for in the sales documents provided to the lender, it won't be conditioned for UNLESS the appraiser sees obvious signs of infestation - in which case - don't you really want to fix those things anyway??
Good luck - and family or not...sometimes especially with family .... consider hiring a Realtor who will work with you on a fee for service basis to help you through some of the sticky, potentially expensive issues.