Why Courts Grant Custody To The Mother

I have a 3 year-old daughter with my ex-girlfriend. I did not know of my daughter until she was 1 years old when I received the papers in the mail. After going through paternity and going to court, I ended up leaving with just visitation rights, no physical or legal custody and paying out a whole lot of cash per month. The courts did not verify anything the mother said. She said she paid over $600 in child care expenses which she had her family members watch my daughter and only paid $300. All the things she said in court were lies, which I questioned the judge about but no one bothered to verify anything. The mother has not been able to keep a job longer than 3 months, currently is unemployed and I still paying her the same amount of child support. My daughter is not getting the proper care she needs, comes to me every weekend with scars and scratches all over her body. The mother's lifestyle is unstable and has had 4 different boyfriends exposing my daughter to all these different men.

The mother has an older daughter from one guy, my daughter and is currently pregnant from her boyfriend. She told me many times that she lives off of the money I give her for child support. Is there a way the courts will see that my daughter is better off with me since I can provide a stable life, have a good job and can provide her all the necessities to live? Instead of giving the mother the money, which I know is not being used for my daughter? I pay for health insurance, pay child support of over $500 and the mother calls me about my daughter not having any underwear. She wants me to pay for the co-payments as well, which she let add up for about 2 years. She claims I am responsible for paying for the co-payments as well. While that is not stated on the court documents. The court documents clearly state "father is to provide health insurance". Any suggestions to go about this situation?