A "right of first refusal" is a provision that sometimes gets added in to a settlement agreement or court order. Such a provision provides that if a parent cannot exercise his or her parenting time for a certain period of time (usually at least an overnight), that parent must offer the time to the other parent before makig other arrangements for a caretaker (like a babysitter or family member).
Importantly, as of 2010, Section 61.13002, Florida Statutes, allows military parents who are given orders to activate or depoly, or who are tempoaraily assigned to military service, for a time period in excess of 90 days, to designate a person to exercise the missed timesharing on the parent's behalf. This person must be a family member, step-parent, or relative to the child by marriage. This means that the other parent is not automatically given that time; there is no right of first refusal. The other parent may only object to the designation on the basis that the visitation is not in the best interest of the child.