I would have suggested that you not contact MIL again, specifically around the sitch. Certainly, one could speculate that by talking to her again, you were able to have her agree not to bring it up with your W. Then again, she still may AND, there's nothing to say that without that comm, your MIL would have left it alone, anyhow.
It's kinda like how we go to a "trusted" confident, or how they say with giving a statement to an officer, that what you say can and will be used against you.
Because even if we believe we have the confidence of someone, we can not control what they do with the information that is shared. Especially if they are fixers and think that they will be helping by sharing or using that information to "help".
In the end, the context of your initial comm with MIL was because D9 was having comm with her, because you needed to leave her alone for an hour and a bit. Your MIL, the smart lady she is, figured something was up. So, ultimately, there were some questions that needed answering... either by you... or eventually by your W...
Perhaps better that it was from you...
So, that said, if it ever comes up again with MIL, just listen and indicate that you'd rather not say anything more at this time.
As for the b-day notice from FB. Again, please remember that these are automated emails that are sent from FB to "friends". Your W is receiving that message because she is friends on FB with tat-boy. In the same way that you would get email notifications of Beyonce regarding her b-day and other goings on in her life, if you were her FB friend.
You are very definitely trying to make a statement by doing anything different than what you would normally do with that email. That statement is likely to show up as either anger or at the very least as some sort of invasion of privacy to your W.
Is that what you want? What consequences are you hoping for?