I disagree for the most part. Diplomatic immunity for actual registered and recognized diplomats and their accompanying family members should stay largely unchanged. If we want our diplomats free from local arrest in the hazardous countries where they represent us, we must give corresponding immunity to all the reprehensible people that end up here as diplomats unless they violate established standards for that immunity.
That doesn't mean we don't apprehend them, send them packing after recognition is stripped, bar them from re-entry, or do other things that we are entitled to do in restricting law breakers. We can further restrict who is granted immunity and extended family members, living away from their diplomat principle should be kept on a very short leash in the allowance of that status, which appears the case here.
As she is not a diplomat or a person enjoying related immunity, she should be prosecuted under Florida State Law.