does the executor of an estate have to live in same state we live in fl.

Thanks for questions. The sons can serve regardless of where the live. Non-blood personal representatives have to be a resident of Florida.
A living trust is better choice than deeding property to family members because of asset protection(homestead) and gift tax laws.

In addition, the spouse of most relatives can be a PR and live out of state. If you want an out of state accountant you can appoint a corporate PR that is not based in Florida.

The statute that governs your question reads as follows:

The statute that I am referring to is § 733.304 related to nonresidents serving as Personal Representative. The Statute specifically states that a person who is not domiciled in the state cannot qualify as personal representative unless the person is:

(1) A legally adopted child or adoptive parent of the decedent;

(2) Related by lineal consanguinity to the decedent;

(3) A spouse or a brother, sister, uncle, aunt, nephew, or niece of the decedent, or someone related by lineal consanguinity to any such person; or

(4) The spouse of a person otherwise qualified under this section.

While the language of the statute is slightly confusing, to answer your question specifically, your mother-in-law's son would be able to serve because they are related.