She would like to move back home to Ohio, but our mother doesn't want to come back. How does she go about not being financially responsible for my mother now? She is also worried that if she leaves her there and something happens to her she will be held responsible.
If your mother is mentally competent to make the decision to stay in Florida, your sister shouldn't be held responsible. She may feel emotionally responsible, but this is your mother's choice. She is an adult.
If your mother is not mentally competent, you may have to get a guardianship (or your sister, or do it jointly) before you can force her to move back to Ohio.
It often pains us when our elders make decisions that we don't feel are in their best interest, but they are not children. They have the right to make mistakes, no matter how much it pains the adult children. So, mental competency is the issue.
Still, looking into all the services offered to elders will help both your mother and your sister make the transition.
Good luck. This is painful for you all.