If a Petition to Establish Paternity has not been filed, the simple answer is yes, even if the Father’s name is on the birth certificate and the father visits with the child and pays child support for the child. As unfair as this is, until a family law judge establishes paternity, the mother of a child born out of wedlock is the natural legal custodian of the child and, until established by the court, there is no legal child custody or parenting plan order.
If a Father has filed a Petition to Establish Paternity in the family law court (which in essence means the Father wants to establish his parental/paternal rights and have a child custody/parenting plan in place with the child) and the mother of the child has relocated with the child, the Father can ask the court for an Emergency Pick Up Order to return the child to the jurisdiction (i.e. the circuit where the case is being held).
Once a Florida divorce or paternity order becomes final, neither parent my relocate more than 50 miles from where he/she is living at the time of the last court order, or at the time of filing a pending action to establish or modify timesharing.
When a parent relocates, even within the 50 mile radius, this can still have a detrimental effect on a child and parents if they have to travel longer to transport the child, especially due to work and traffic schedules. What can be most devastating to children is being forced to change school districts, so it’s definitely in their best interests to keep them settled in the school district they are in assuming it’s possible.