Sounds like the pseudo-instructor has some qualms about signing something that says she's not receiving money. Since that's probably incorrect, and may even be fraud.
Look at it this way - she won't accept the liability of the bossy mare on *her* property, but wants you to accept that liability while she teaches lessons at your place. Last time I ran a horse business, boarding was 95% percent overhead and a tiny profit if you were lucky, and free lance teaching without insurance at someone else's barn is 0% overhead and 100% profit.
Tell her politely that your attorney and insurance agent have advised against it; and that you can't accomodate her.
The boarders can either 1.) take lessons with you 2.) haul offsite to their lessons or 3.) move their horses, which, BTW are usually the standard options.