Why's there still tartar in between the tooth after having it polished and scaled by the dentist?

Visually or x-ray: A dentist can visually see a crack or take an x-ray to verify a crack. Sometimes by symptoms such as the tooth hurts only on chewing can verify a vertical fracture which does not show up on an x-ray.

Find a new dentist: If its really tartar (calculus) left behind then its time to find a new dentist. To be honest most dentists aren't great at scaling teeth. I would look for a dentist that uses a dental hygienist. I always have a hygienist clean my teeth over a dentist.