My daughter's father has never been a concistant part of her life. She is 7 and a half now, and he's been out of her life more than he is in it. His mother has made it very clear to me that if I try to get full custody of my daughter, she will fight for custodial rights as a grandmother. My daughter does well in school, she is in a dance/acting class, she has a very good home here with me and her step-brother. She is established here. Can her grandmother do this? Even though her father has made it clear that he is incapable of being a father?

What type of custody is there now thought he court ? Is the father paying court ordered child support.

Grandparents are allowed in some US states ( but not many at this time) to have visits, just visits, every other weekend perhaps or a couple of days a month.
She can not get "custody"

Fr Chuck is right, in the United states grandparents have no custodial rights whatsoever. The only problem would be if she paid for the lawyer and fought for custody in the name of her son, the catch there is she would need him to go along with it.

This is a very complicated issue. I don't understand why you already don't have full custody. If you are sharing custody with the father's mother only, legally YOU DO NOT HAVE TO DO SO! Lacking many details, I can tell you this, from my own personal experience... Grandparents DO NOT have legal rights over either parent. If one parent is proven unfit (which is very hard to prove) or dies, the other parent will assume full legal rights over their children. Forgive me if I cite it wrong, but several years ago the Supreme Court in Granville vs. Troxel, ruled only rare circumstances will allow a court to grant grandparents set visitation if the custodial parent is perceived to be acting reasonable with visitation. However, normally, grandparents visitation falls under the visitation time of the non-custodial parent. Courts do not set legal visitation rights as I said, except only in rare and unusal conditions that are literally chiseled in stone. You sound like a good mother being bullied by the grandmother. You should Google your state's family law statues, try to understand them, trust me, and tell the grandmother you will allow her to file if she chooses, but either way, she IS NOT your daughter's PARENT! Good luck and don't be afraid to fight her, just be informed... Google always has an answer for me. God Bless the Children as we all are.

WRONG!

In some states, grandparents DO get rights if they fight for them. In Indiana in particular, grandparents can get rights over children that their child has placed for adoption---so the child isn't even legally related to them, but they can still get visitation rights!

So--a LOT depends on the location of the OP. This is a law that varies a lot by state, and without knowing where the OP is, we can not give her an honest legal answer.