What decision making rights do I have as the custodial parent and why?

I have a daughter who is 5 while I was pregnant he called me lots of bad names and said the baby wasn’t his. She was born I named her with my last name but naming him as the father on the birth certificate. He signed it a month and half later he got a DNA test done she was his. He now pays child support. He got a DV charge and ended up with supervised visits and I got sole decision making responsibility. For about 5 years he has a poor track record for his visits put it this way he had 110 available visits last year and showed for 44 of them that’s how it has been for almost 5 years. In January of this year we went back to court and he now has unsupervised visits. He is ordered to help me pay medical dental vision etc. and he will not he says it’s my problem. So I am having to pay 100% of medical cost he has also had her on medical insurance 3 times and has dropped her 2 times he puts her on ins when he is up to something for example I got served to go to court in January of this year on sept 4th of last year which was a Saturday that wed he gave me an insurance card. Now he wants the court to change her last name to his he put on the petition to acknowledge that she was his daughter and most kids carry their father’s last name anyway to me that’s not a good reason what about me and my rights I have been with this child 100% thru thick and thin. I am the one who makes everything ok for my child when her dad jacks up. When my child asks me why her dad left early or why her dad didn’t come back or why her dad plays with his cell phone all the time or why her dad doesn’t give her medication. I am the one who takes care of it and tries to make everything ok. I am always fixing everything. Now that he has unsupervised visits he has the I'M THE DAD ATTITUDE and she is mine and I will do what I want with her. I feel he looks at her as a possession and not his child. What can I do I am the custodial parent and have sole decision maki