You may engage in any form of financial discovery, requests to produce, interrogatories, depositions, etc., in order to determine and show to the court that your husband is improperly diverting funds to his current wife in order to avoid paying child support.
Regarding your question about Florida Rule of Civ. P. 1.560, it does not apply. There is a specific counterpart, Florida Family Law Rule of Procedure 12.560. Subdivision 12.560(d) applies to final judgments that award money damages.
The financial relationship between an obligor, who owes but stopped paying alimony, and someone else such as a current wife is discoverable. That doesn't mean all of the new spouse's financial data are discoverable; discovery is limited to the financial relationship between the former spouse and his current wife. Because the alimony obligation isn't a final judgment which awards money damages, avenues other than 12.560 may be available to discover some the information you are seeking.
Check with a tax advisor on your specific other question about 1099s.
Please note that this response is not intended to create any attorney-client relationship and is only based on the limited facts given. The response might change should additional facts be learned and should not be relied on as legal advice. It is recommended that you consult with an attorney who can properly assess the situation, as well as all pertinent facts, prior to taking any action based on the foregoing statements.
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