Yeah, I think your family doesn't know what's up.
Here's an extensive breakdown of Florida sex offender laws: https://screenandreveal.com/florida-sex-offender-laws/
They talk about frequency of reporting, requirement to report travel plans, and even sex offenders that come in from out of state. And they are required to report within 48 hours if they will be there longer than 3 days. They can't move near a school (but don't have to move if a school is built near them).
But that's it. Nothing about not being able to move there.