Child support/full custody? Help please?

OK recently me and the child of my mother had a disagreement i guess you could say. She got upset that i don't get my daughter more often. I'm working two jobs and going to school full time right now so I see her as much as possible. But now shes being spiteful and wants to put me on child support and wont let me claim my daughter on my tax return. I'm not really worrying about being on child support because either way I would be supporting my child but how exactly do they calculate how much money there gonna take from me for child support? I live in Florida and she and the baby are also on medicaid or medicare one of those. Doesn't that mean some of the child support would go back to the state? And also seeing as how she is unemployed and got arrested for a warrant she had from running a red light a while ago and for driving without a license is there a good chance I could win a custody fight? Her most recent job was bar tending at a strip club... I don't think the courts would favor that too much. I'm basically trying to see what my options are. To me shes not a very fit mother but would those things i mentioned be enough to show it? Her most recent job was bar tending at a strip club, she got arrested last week, shes unemployed now, no high school diploma or ged. I truly believe I could be a much better parent for my daughter but dont want to start up a custody fight and cause more damage. We have never been married or anything like that.