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Kentucky does permit the recording of a conversation as long as one party to the conversation is aware that it is being recorded - in other words since your son in law knew it was being recorded it would be legal - however, if you and he were having a conversation and a third party was recording it without knowledge of either of you, then it would be Eavesdropping and illegal. If a third party was recording with permission of one or the other or you it would be legal.
It would be admissible as evidence - however, keep in mind that evidence is at the discretion of a judge as to whether they want to allow it and would be based on its importance.
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