I think the 'safest' way is the sincere way. Wait until you're alone with her and the time is right, tell her how some of what she's doing points to the possibility that she may be suffering with PMS. I know you haven't done it, but I definitely wouldn't let anyone mock her for it, like her sisters, sometimes siblings can be pretty harsh.
There's no way I agree that video taping her is a good idea, that's
very invasive and counter-productive, IMO. If you really want her to get mad and remain in denial of having a problem at all, and resenting you to boot, something like that will do it. There are other avenues to deal with this in a more loving way between mother and daughter.
There are some natural ways to help ease the symptoms that she may be interested in, you can tell her about using Lavender Oil when you have a private talk with her, if she decides to try it, you can keep it your little secret with her. You can get a small bottle at the local health food/vitamin store. That way you show her that you're a friend who wants to help. Here's some info, I'm sure there are other things that will help too...good luck.
http://www.greenmedinfo.com/blog/lavender-aromatherapy-proven-calm-premenstrual-emotions
The only thing I used for menopausal symptoms like hot flashes was Red Clover Blossom, which is a supplement that is also good for relieving PMS. As with all supplements, best to research side effects and drug interactions if she's on any prescription meds.