Likely the judge would not admit the evidence. I would NOT start worrying about every little thing your ex threatens to blurt something out in court.
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They could always make the claim, and they may be able to introduce a phone record of a call being placed or received. However, the details of the conversation would be subject to evidentiary rules and if the Judge allowed testimony as to the conversation, the Judge would independently weigh the veracity (truthfulness) of the parties during testimony.
Beware. If the telephone call originated from over a state line, your recording it is probably a felony.
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