Full Custody advice in California?

To make a long story short, I need help. My son's father tells my son he'll come pick him up, but rarely ever does. He is constantly letting my son down. He's never paid child support, he only sees his son once every month or so, and when he does take my son, he is always drinking alcohol. He dislocated my son's arm recently because he has no idea how to take care of a child, and now my son doesn't want to go back. My son is only four years old and he is highly allergic to dogs and has asthma. Because my son's father refuses to get rid of his dogs, he sends my son back to me smelling like cigarettes, barely able to breathe from the dog hair, and a rash all over his body. A friend of my son's father said that he saw him kick my son in the head as a punishment. My worst fear is that I'll die and my son will end up with his father. I really want to get full custody, but I'm afraid if I lose, my son's father will take start taking my son more often than he already does out of spite. I don't know what to do. Is the information I listed enough to win a custody battle? I want my parents to get my son if anything happens to me.