Have you contacted the Clerk's office trying to get a copy of the Final Judgment? It seems very unlikely that if the case were finalized weeks ago that it would not be filed with the county yet.
If there is a provision in the judgment that says you should have the opportunity to have the children if she is using a babysitter, then you would seem to have a good case for the courts to get involved, especially if your children are being exposed to a sex offender.
Your fact pattern suggests there was a trial so is the final judgment still pending? i.e., the attorneys may be drafting competing final judgments for the judge to consider and maybe the final judgment hasn't been signed yet? You need to provide more facts. Contact your attorney and ask what is going on with the final judgment. Also, go the clerk of court or check online to see if a final judgment has been entered. If so, you can get a copy from the clerk.
Legal disclaimer: I'm only licensed in FL. Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
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