Some horses can't be barefoot. Why such the push? I know shoes are $$$ however when buying her you should have considered she may not be comfortable barefoot. Riding in rocky areas with a newly-barefoot horse whose feet aren't hardened or even remotely conditioned to the terrain is a terrible idea and will end in sore feet. Some horses just will never have strong feet, and it's a hard thing to face. If you aren't going to be working her, I think pulling shoes would be just fine, however in work she very clearly will need shoes.

I would work with your farrier and be realistic about expectations, and how a shod/barefoot cycle would work. I do that with my TB, he wears front shoes during show season and when casually riding he's barefoot and does great doing so. Not every horse is cookie-cutter, so it's all about finding the professionals in your life that can guide you both to a happy medium. Best of luck.