Legal Question in Family Law in Ohio

In Ohio, there should be a court order in place, either in domestic court if the two of you were married, or in juvenile court if you were never married, which determines what the custodial arrangement is between the two of you. If he wants to change that order, then he will have to go before the court and convince the judge or magistrate that this is in the best interests of the child. You will have the right to attend that hearing and give evidence and argument to the contrary.

Your points about how he has kicked her out of his house in the past, how he has minimal involvement in her life, and how the daughter would feel bad about this (losing all of her local friends and relationships, switching schools, church, etc) would all be important information for the court to hear in making its decision on who it is best for the child to live with.

If you can't afford an attorney in this matter, you might want to look about for a local Legal Aid Society, or perhaps if there is a law school nearby you can ask to speak with someone at the legal clinic who might be able to represent you.

Further, you could petition the court to appoint a Guardian Ad Litem. A G.A.L. is an attorney who is appointed by the court to represent the interests of the child. You can then work with the G.A.L. (always understanding that he/she works for the child, not you) and convince the G.A.L. to advocate for the child that staying with you is the best thing.