Is it hard to prove neglect or lack of supervision in court in my daughter's mother?

I'm taking my daughters mom to court for custody as she leaves our daughter with people who are bad news and does not supervise her. I found my child playing near the road and her mother nowhere in site. My child was also burned badly on her hand in the past and no one knew what happened. I took her to the hospital and called the police. My daughter is always at risk of harm. How can I win sole legal custody and primary residence?