Can a child still get emancipated from her birth mother and step father if her father is fighting for custody?

No, if there is a custody dispute being heard by the court, that needs to be settled before any early emancipation petition would be accepted (if at all). There is a great misconception as to a minor receiving an early emancipation decree. It is not simply a matter of signing a paper and getting the request granted. Most states have "safe guards" within existing statutes which make it very difficult to become legally emancipated. I have doubts as to how many minors who claim they "did it w/o a problem" are being completely truthful.