Fainting can be caused by a brain tumor, brain hemorrhage, stress in the body, medications, or epilepsy in some cases, so I'd see the neurologist to rule all these out. Diabetes can also cause this, if your blood sugar is too low, and so can dehydration and heat stroke.
I have been fainting since I was a kid, I have seen cardiologists and neurologists and done every brain and heart study you can imagine, and I ruled all the natural causes out. In my case, it is psychosomatic. I faint when I see carnage and gore, or when I am in severe pain and it is close to one of my nerves, which enhances the pain even more, but there's always a root cause, it doesn't just happen if I am at work or driving (unless I see roadkill).
I wouldn't say I have total control over it but I have more control than I did when I was younger although I cannot always keep it 100% at bay. I know when it is about to come and I can take precautionary measures now to ensure I don't fall (I would always fall backwards on pavement and hit my head). I can also tell when something will affect me as it happens on the spot, and tell people around me that I will most likely faint as I feel like it is about to happen, so they don't freak out and/or can make accommodations for me.
I would definitely see the neurologist to make sure she is healthy and then worry about the dentist and the cosmetic aspect later. Her health is more important than a cracked tooth (they have veneers to address that).