I assure you the insurance company doesn't think it's a gray area at all. If you are instructing that is commercial activity and your normal owner policy will NOT pay out. This is also often the case if you are instructing in the student's own airplane (many CFI's and Owners don't realize this - CFI's need to CYA).
To provide some limited instruction in your own airplane look for "CFI Owned" policies which are usually 1/2 the cost or even less than full commercial coverage. To go from a personal policy to a commercial policy will increase your premium 4-10x. You should also find a respectable broker, explain exactly what you want to do and have them shop many underwriters, the programs offered by different underwriters vary a lot and some might have a program to fit your needs better... but you really need to know what you want to do first.
In general, assume that your particular use case is not covered by insurance unless you can specifically see that it is covered in a specific insurance policy (and even then you may be in for a fight when a claim is made). That's how the underwriter will see it when you go to make a claim... just the way it goes
I rent my own airplane out to students and other CFI's so I've been through this. All I can tell you is that it's frustrating and expensive, but if you want to do it there are ways.