If one spouse has timesharing/custody and the other has no timesharing custody, can they move out of the state?

Under these circumstances, the parent with no time sharing must go to court and demand that the child remain in the state of Florida. You have to remember that even if you are not awarded any time sharing by the court in a divorce case, you are still entitled a must have a pathway of actions that you can take to have your time sharing reinstated or put into place. It will depend upon how far along you are on that pathway but nevertheless, a parent with majority time sharing must still always receive court permission before they leave so you entitled at the very least to have a hearing on this issue. But unless you go to court, then the other parent is just going to be in another state and you have no contact with your child.