I'm always amazed at people who "prove" they love you by making threats to withhold that love. I refuse to be emotionally manipulated by anyone - alcoholic or not. If I was comfortable with the idea that my actions could result in some family members cutting me off, I'd carry on and live my life.
Only you know if the situation is safe. For the record, telling someone you will disown them if they don't do what you want is also verbal abuse. I wish you all the best. Enjoy your son on this mother's day.