what is easier in Florida terminating parental rights or file for abandonment to get full custody and name change?

Thank you for your question. You didn’t mention the age of your daughter. It could make a difference to your question if she was two years old or fifteen years old.  I am going to assume she is a pre-schooler. As you referred to your past relationship as your “ex”, I am also going to assume that you are divorced. This is also a major factor in your question. If you are divorced and your “ex” is the legal father of your child as recognized in the Final Judgment with timesharing rights and shared parental responsibility, then you will have to seek court permission to relocated to Michigan or obtain a written consent to the relocation from your “ex”. Florida’s parental relocation law (Chapter 61.13001, F.S.) carefully defines the procedure for relocating out of state with a minor child. You can Google the statute and carefully read it. Of course, the assistance of a qualified family law attorney would be highly recommended. If you were never married to your “ex”, and a paternity case has not been filed and no other legal determination that he is the father of your daughter has been established (as in an administrative child support action), then the limitations on your relocating should not apply. Again, you should consult with a qualified family lawyer to understand your rights and obligations under these two scenarios - divorce or paternity.