You absolutely 100% have a leg to stand on... probably two. Courts in Ohio are going to evaluate between two biological parents based on what is the best interest of the children. Because you were not married to this woman when your daughters were born, Ohio law does not presume you are the father and your rights are contingent upon you signing your daughter's birth certificate or an affidavit of paternity. Have you done either of these two things with respect to both girls? If you can also file a court action to establish paternity.
If paternity is established, file for custody in your local juvenile court. You will undoubtedly need a lawyer to help you with this but this is the first step to getting custody of your daughter. In the meantime, if your ex wants to leave, let her, but inform her that under no circumstance are you leaving and under no circumstance is she taking the girls with her.
Good luck to you
Don't worry about unfit standards, as you don't need to prove that at this time. You are the father so you are on the same level as the mother. The court test will be the best interests of the children, not the unfitness of the mother alone. You need to prove that you are the better parent to rear the children and that mother is in no position to have primary responsibility for caring for the children.
Find yourself an attorney and get into court asap so that you do not lose where the mother is at and to get orders in place to prevent her from denying you access to the children. If the mother disappears from your view, it will take a lot of effort to go looking for her to get the court case started.