I really respect you for trying to find answers for you mother's migraines. From your post, it seems that you may have some misconceptions about migraines. First, some migraine sufferers have an "aura", which is any combination of symptoms, like seeing flashing, which precede a migraine attack, as sort of a warning system. This is also known as a "prodrome", which comes with a "classic" migraine. If a migraine sufferer doesn't have the "aura", they have "common" migraines. Either type of migraine can last for days, especially if not treated.
Cluster headaches are a totally different animal. Cluster headaches are very intense headaches, which generally only last a few hours. These headaches come in groups, several in succession, but then stop for period of time, sometimes weeks or months between attacks. From your description, it sounds like your mother has migraine attacks, not cluster headaches.
You mention her having "mania". Has she been diagnose as manic-depressive or bi-polar? If so, is she taking any medication to control the mood swings? Is she taking anything for her migraines? Migraineurs should be on a preventative medication, an abortive medication to take when a migraine starts coming on, and an emergency medication for breakthrough pain. What medications will work for your mother should be worked out with her primary care physician or preferrably a neurologist.
TMJ can be a major trigger for migraines. I am personally dealing with a bad case of TMJ myself, and I'm getting 2/3 migraines a week. My migraines are so bad, I'm having to get a shot for pain at least once a week. I have some bad dental work which triggered a really bad case of TMJ. I can't get my teeth fixed until the end of the month, so tomorrow I'm going to see a doctor that is also a dentist. He specializes in TMJ, so hopefully I can get some relief from this horrible pain. Maybe you can find a similar doctor for your mother.
I takes a great amount of compassion to reach out and try to find help for your mother. I hope this information gets you started in your quest. Please let us know how things are going. We'll be glad to answer any questions you might have, and nothing is out of bounds.