If the children grow up with positive feed back and with an education and understanding of the disease they will perhaps make other choices. If they are brought up with bitter resentment and the thought that their father was a weak coward, their self-esteems will drop and it will have a very negative effect on them during their entire lives and the choices that they make. You are clearly in a lot of pain and feeling a lot of anger, and of course are now taking on the responsibility of Tony's children. There is a scheme to all of our lives. Perhaps you will change the outcome of Tony's children, whereas if he had raised them, they may have turned out exactly like he.
Alcoholism has a way of repeating itself through generations.
Try to forgive Tony for his weakness of will and try really hard to allow your love of Tony to rise you above the anger. Remember alcoholism is a disease, not a chosen vocation. I wish you peace of mind, strength of will and grace.