Thanks for using the forum. I am happy to address your questions, and my answer will be based on the information you provided here. Please make sure you recognize that this forum is for educational purposes only, and it does not substitute for a formal office visit with your doctor.
Without the ability to examine your mom and obtain a history, I can not make specific recommendations. However I will try to provide you with some useful information.
I am not sure if your mom has been diagnosed with trigeminal neuralgia or if there is another cause for her facial pain, so I will discuss trigeminal neuralgia treatment as this is the most cause of facial pain. It sounds like she has failed some medical therapies such as anticonvulsants and neurontin; there are a few other medications that have been tried and are helpful in some patients such as cymbalta, but the most research is available for the anticonvulsants such as carbamazepine (tegretol).
Regarding surgical procedures, one is termed rhizotomy, which is involves an intentional selective injury to part of the trigeminal nerve system called the Gasserian ganglion, with the goal of preventing nerve impulses from passing along the nerve.
Micro-surgery for trigeminal neuralgia involves attempting to remove compression on the nerve such as a small artery. Sometimes, a more radical approach is required such as partial or complete cutting of the nerve. With these types of surgeries, certain complications sometimes occur but are infrequent.
Finally, gamma knife treatment, which is a non-surgical treatment involving radiation, is sometimes helpful but the effect may be delayed by a few weeks to a few months.
Finally, trigeminal neuralgia can be treated with electrical stimulation. This has become increasingly more researched in recent years. The Gasserion ganglion (part of the trigeminal nerve system) has been targeted as the site of stimulation. A temporary stimulation is applied and if helpful to the patient, a more permanent stimulator is placed.
Surgical treatment including stimulation for trigeminal neuralgia is usually done by neurosurgeons, though in some institutions and some procedures anesthesiology pain medicine specialists are involved as well. Often, a multi-disciplinary approach (treatment by doctors from different specialties) is most beneficial.
Thank you for this opportunity to answer your questions, I hope you find the information I have provided useful, good luck.