Whether a piece of evidence is admissible depends upon several factors.  Whether a voicemail message is admissible depends upon its content, what you hope to prove with it, and the relevance of what you hope to prove to the case.  The fact that you are in a family law court probably doesn't matter, but it may in some states and you haven't said what state you're in.

The message should be admissible in the situation you describe, since it is very relevant to whether you violated an order and thus whether you are in contempt.  Be prepared to testify not only that the message was left for you but also how you made the copy for the court to hear and where that copy has been since you made it.  If your voicemail service announces the date and time of the message be sure to include that in the copy. If you can keep the original message on your voicemail and then dial it up for the court, you will be able to avoid a lot of questions about its authenticity.  And if the message is from a machine on which you set the date and time yourself, expect to be cross-examined about the reliability of that information.

Recordings of conversations that the other person did not know were being recorded are often inadmissible in order to protect people's privacy.  Someone who leaves a voicemail message clearly does know he is being recorded and can't complain that you still have the recording.

Let us know how you do in court.