After much digging around, here is what I have found, for what it is worth.
My dilemma is I am part owner in the aircraft in which I instruct however our flying club's insurance policy does not cover me when acting as CFI.
I found that NAFI will not cover me in their non-owned policy because of my part ownership, regardless of how diluted my share is.
AOPA, however, will cover me in their CFI/non-owned policy as long as my ownership is less than 1/19th. Since I have only 1/38th ownership, they will cover me with no problem. I guess it will be AOPA...
A real headache, all of this, but better be safe than sorry.