Is it right for me to keep my mother seeing my children?

I haven't spoken to my mother for 10 years. She has never met my 2 younger children. I broke off contact with her because I couldn't handle her drinking anymore - she's been an alcoholic for most of my life, and still drinks. I couldn't and didn't want to be around that anymore and chose to not have her in my life anymore - and I have been so much happier for doing so. But having said that, my mother has moments of being quite normal and lovely (even if she does drink non-stop), and my father and other people have said to me that it's not right to not have her in my life or my children's lives. My sister still sees her and her children have contact with her, but she lives out of town and it's only once or twice a year. When my mother was in my life she would turn up on my doorstep unannounced 2-3 times a week, and call and argue with me about anything and everything (which is quite a common thing for alcoholics to do). So do you think it is wrong of me to cut her out my children's lives like I have? I believe it better for them not to be exposed to such a physically and mentally unhealthy person, in fact, I think it would be detrimental to them to have her in their lives. I've told my mother that if and when she stops drinking I won't hesitate to let her see the kids, but until then I just think that she's too unstable a person to be around my kids...