AITAH for considering ending the relationship because he asked our child to lie to me for months about a female work colleague?

His preferred way of communication is withholding information – if I don’t know I can’t get hurt. I fully disagree with it and I’m very transparent about work colleague interactions both with males and females.
About two years ago, I noticed a female colleague was messaging my husband frequently. I didn’t see the contents fully as he deletes everyone’s messages. I expressed my concerns and said I don’t have a problem you having a professional relationship with her just don’t delete your messages if I ever want to see, to which he agreed.
My child spends some time at his workplace due to my job being in a different city.
Now, I’ve just been told by my child that he has been “deleting conversations” with her and has explicitly said, “we don’t need to tell mum”. This has been going on for a year. They have spent time together 4-6 times.
The woman in question even made a comment about someone saying that someone said to her that our child looks like her and my husband, in both their presence. I’m told by my child that my husband just laughed it off.
I have been having an intuition about something being off but did not think he was asking my child to lie to me so she can hang around with this female colleague.
When confronted, he accepted it was wrong but tried to say I have jealousy issues that’s why. I’m baffled, I was right about this female colleague? Why would anyone say that randomly about my child? (She doesn’t look like her one bit), even if someone did, why would this woman feel the need to repeat?
I also noticed my child not sharing a lot of personal stuff with me when this was happening. I feel betrayed on so many levels.
AITAH and AIO to think involving my child in this behaviour is not only unacceptable but also unrepairable?
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