Need help when she drinks and threatens to commit suicide is my mum a alcoholic?

She is depressed: Your mum is depressed; she may be an alcoholic; & she definitely needs help. People think that alcohol will make them feel better, but alcohol is a depressant. Anyone who is depressed should not drink. It will make them more depressed & more likely to commit suicide. Get your mother to a therapist or emergency room asap. They'll figure out whether she is an alcoholic & help prevent her suicide.

Problematic drinking: I am sorry, but i can't diagnose your mother. It is clear that this is a real problem. If she is in danger encourage you to bring her to the er or contact local police to assist with getting her urgent help if needed. I suspect that if she repeatedly threatens suicide that there is more going on then alcohol. When she is not intoxicated - broach idea of her seeing her physician or going to aa.