I kinda agree with Joe... down here in NC is pretty popular to share your land with your neighbors. Most of the farmers here are quite passive about letting us ride through their fields as long as we don't mess anything up and pick up after ourselves (which the entire horse community does from what I have seen). Several of my horse neighbors graciously let Indie and I wander through their wooded trails that they too painstakingly cut... but I've met up with them before and they say they love meeting other horse people out on the trails, it keeps them company and makes them feel appreciated for the lovely riding paths.
I suppose if I were you, I'd try to make friends with her.... but then it just strikes me as odd (from my background and standpoint) that someone with large trails would be so hesitant to share, does your neighbor have any of her own trails? I'd probably feel bad for her and be even more likely to share if she didn't have her own areas to enjoy the great outdoors from the back of a horse.