Hi WW you might want to post this in the Friends and Family of Alcoholics forum where you will meet many people who know what you are going through.
Time will tell whether your mother can moderate her drinking but many A's have to give up completely. It depends how far in she is. And yes, you would expect her to be quiet and snappish because she probably desperately wants a drink. Giving up drinking completely causes the craving to diminish over time, but have the odd lunch with alcohol may keep them alive.