Several things:
1) Again, NORMALLY, the estate is probated in the state where the decedent has property. Did she own REAL property in Florida??
2) I don't know of a statutory REQUIREMENT for filing in Florida.
3) If there is not a court ordered executor (personal representative), anyone can apply to the court to be approved as such and would then have the RIGHT to distribute the estate per law.
Since you say that this is a will... What state is named IN the will.