I would definitely recommend that your mother get additional evaluation to try to figure out what is going on. It sounds like some of the really bad things have already been ruled out, because a CT scan or MRI scan of the brain would detect a brain tumor or something like that.
However, there are many causes of chronic dizziness. If she hasn't had a problem with her heart ruled out, that is definitely something that should be checked off, likely with a visit to either her cardiologist
or her primary care doctor
Assuming that is negative, the next stop might be a ear, nose, and throat doctor. Many of the chronic causes of dizziness are related to inflammation of the inner ear apparatus. These conditions include labyrinthitis, vestibulitis, benign positional vertigo, and Meniere's disease (although Meniere's disease is less likely if she had a normal hearing test). The ear, nose, and throat specialist
should be able to evaluate for these conditions and help determine whether any additional testing is needed. Many cases of chronic dizziness do not have any specific cure, but medications to help control the dizziness may help your mother out quite a bit.