Does Governor Ron DeSantis have to the power to stop Trump's extradition?
If any criminal charges were brought against Trump for violation of laws of the United States, the FBI would deal with the issue and the State of New York is not relevant to that case.
New York Attorney General Letitia James is “actively investigating the Trump Organization in a criminal capacity”. Politico
In the event that the State of New York were to charge Trump with a violation of state law. DeSantis could delay, but not stop, an extradition request from New York. Under Florida statute 941.04, Governor DeSantis could deny extradition; but note that the statutes were written in 1941. At that time, Kentucky v. Dennison (1861) was the ruling decision of the court. In 1987, Dennison was overturned by Puerto Rico v. Branstad. The decision in Branstad means that, if Governor DeSantis were to refuse extradition, New York could request a federal court order to require the governor to arrest Trump then release Trump to agents for New York.
Florida Statutes, Uniform Interstate Extradition
941.02 Fugitives from justice; duty of Governor.—Subject to the provisions of this chapter, the provisions of the Constitution of the United States controlling, and any and all Acts of Congress enacted in pursuance thereof, it is the duty of the Governor of this state to have arrested and delivered up to the executive authority of any other state of the United States any person charged in that state with treason, felony, or other crime, who has fled from justice and is found in this state.
History.—s. 2, ch. 20460, 1941.
941.04 Governor may investigate case.—When a demand shall be made upon the Governor of this state by the executive authority of another state for the surrender of a person so charged with crime, the Governor may call upon the Department of Legal Affairs or any prosecuting officer in this state to investigate or assist in investigating the demand, and to report to him or her the situation and circumstances of the person so demanded, and whether the person ought to be surrendered.
History.—s. 4, ch. 20460, 1941; ss. 11, 35, ch. 69-106; s. 1597, ch. 97-102.
Puerto Rico v. Branstad
Puerto Rico v. Branstad, 483 U.S. 219 (1987), was a case decided by the Supreme Court of the United States that ruled unanimously that federal courts have the power to enforce extraditions based on the Extradition Clause of Article Four of the United States Constitution. The decision overruled a prior decision in Kentucky v. Dennison, which had made federal courts powerless to order governors of other U.S. states to fulfill their obligations in the Extradition Clause.