Want full custody-how do we prove a mother unfit?

We have doented things since Dec. about my husband's ex being unfit for my two year old step daughter however, I have no clue if they will stand up in court. There were a TON of things prior to Dec. and people kept telling us to doent but I was trying to be optimistic and thought things would get better. They did not. In the four months since I've began doenting we have acquired PAGES of various things, just from her dropping off the child and the child's condition when she comes over. The mother is not a drug addict or abusive to our knowledge but she is under 21 and drinks. She has also been with at least 10 different men in the past 2 years and is now living with her boyfriend and they are supposed to buy her mother's house that she is living in (rent free of course... even though we have a mortgage and pay child support and she claims it is not enough...). In addition to that the baby sleeps in the basement while baby mama and her boy toy sleep upstairs where the baby cannot be heard or grabbed quickly in the case of emergency. She stated that the baby goes in the basement and plays 'for hours' and comes upstairs when a dvd needs changed (this is neglect to me). She basically said that she sent the baby to bed without eating her vegetables. The child did not eat them for lunch so then baby mama tried to make her eat them for dinner while she ate white castle. The baby would not eat the vegetables (she's 2, she's picky, I give her v8 juice and lots of fruits) and so baby mama put her to bed. There are other things such as the mother having a pitbull bull mastiff mix that almost attacked my husband and has left scratches and bruises on the baby, baby being dropped off in 50 degree weather with nothing but a thin long sleeved shirt (no coat), bad yeast infections that were not mentioned, baby being in way too small of shoes or way too big of shoes, baby being unbathed, being in the same pair of socks for a week straight, old nasty diapers (she actually dropped baby off at 8:30 in the morning in a full pull up and said she went potty that morning so the baby still had the overnight pull up on), and a ton of other things. I do not think the mother tries to be bad I think she is really just dumb. Would we be able to gain custody? Thanks.