In Mar. of 2010 my daughter and her mother were taking to FL from IN by my child's grandmother.At the time my daughter's mother was unaware of the laws in IN and didn't realize she was leagally emancipated once she became pregnant.It took me until Aug. of 2010 to get down here to FL to be with my daughter.I'm not currently on the birth certificate but I have let the state of FL know I am the father.Now they are charging me with child abandonment... Is it possible to get these charges dropped and Could I charge my child's grandmother with kidnapp?

They can attempt to get you charged with abandonment, but I am thinking it has not happened yet, right? Her moving, you staying put is not abandonment. Did you communicate at all during the last 5 months and did you contribute any money to help feed and cloth the child?

... Could I charge my child's grandmother with kidnapp?

I don't see how. Who would have been the kidnap victim? Did she take either your daughter or your daughter's mother against her will?

Do you mean custodial interference? Was there a custody order in place which was violated? Your child's mother, was arguably emancipated, at least under Florida law, so if so, she had the right to take her child with her and (assuming no custody order), it wouldn't be a violation.

Not sure exactly but they can try and charge you by lying to the courts or authorities. ( or tell just their side of story)
So you hire a good lawyer, and let them handle any statements and answers about the issues.