Get yourself a binder, take notes like CEO said with details, date, time, where you were and all that. If you give her any money you need to give her everything in a check or a money order and make a copy of it before you give it to her with the words "CHILD SUPPORT" written on it clearly. Keep these in the binder. Also a judge is going to give you a verbal smack down for not doing this sooner if she is so "unfit", so you better come up with an explanation for that. Has she been arrested? Had the cops called on her? You can get convictions and I believe arrest records from your state bureau of investigation. Just google "(your state) Bureau of Investigation" and it should come up. They will allow you to print it right away. Put that in the binder. Then go to the police stations in the city or cities that you know the cops were called on her. Have her name, and birth date or SS#, usually birth date is fine and an address were the incident took place. If there is no report, then ask for the dispatcher transcripts. That is all the communication between you, the cops, and the dispatcher. Put that in your binder. Document the condition of the child when you see her, is she dirty? Clothes ripped? Do you get her hungry? All of this goes into the binder.
Then you build a support group to help you with the kid. Mom, Auntie, Sister, whatever, you need help raising her. Family is important and it can consist of anyone around you who is good, stable and balanced, even close friends. Are you in college? If not then get certified in something at a community college (cheaper than vocational school). Go to your local labor department, as a single dad there should be grants and programs that will help you pay for it. This way you don't have to be gone for 15 hours a day and you can raise your daughter.
And finally, change the way you look, speak and carry yourself. You have a child now, your days of being a kid are over. Pull up your fucking pants, take those stupid fake square diamonds out of your ears, and no more wearing stained wife-beaters in public. Speak properly, no slang at a job interview, at work or at home in front of your little one. Kids learn how to carry themselves from us. And trust me it will help the both of you in the long run. You need to stop being a pussy and crying, but I'm the man. Yea you got an uphill battle, but if the mom is as bad as you say, it's one you need to fight.