Yep, if you have migraine without headache with aura (aka painless or acephalgic migraine), vertigo can most certainly be your aura (aka vertiginous migraine or MAV).
Most women find that, post-menopause, their migraines diminish. A minority find the opposite to be true. I'm not too familiar with migraine and the period just prior to menopause. You may want to seek out and consult a headache specialist (a neurology subspecialty). Who knows, maybe hormone replacement therapy would be an option???
That's very interesting that diet coke makes you feel better. The vast majority of people have the exact opposite reaction. It contains a bunch of triggers, including aspartame (neuro-excitatory molecule). But if it works for you... more power to you.
Now I've always heard that soda is bad for the bones. It chelates out calcium. If this is true... and you are extremely sensitive to calcium fluctuations I could see how diet soda may help. A lot of us migrainuers find that taking supplemental magnesium (citrate or malate), helps with the migraines. You should ask your neuro or GP about this (we usually start off taking 400 mg and build up to b/w 800mg and 1.2g / day). It may take upto a 3 months to notice a difference.
Best of luck!