You need to understand their dysfunctional family dynamic - so that strategically you don’t feed into it and become another cog in their enmeshed system.
You are at risk of being really set up here.
The MIL is goading YOU.
Know that. This is all about her reclaiming and being possessive about her DS. YOU are the enemy and she is setting a trap.
The WORST thing you can do is kick off at her / call her out - that’s EXACTLY what she wants you to do - to get angry so that she can do the usual manipulative DARVO (deny, attack, reverse, victim and offender) process to paint her as the victim and you as the villain.
There will be tears, histrionics, weeping and wailing - full on dramatic pantomime.
She will dine out on that for YEARS and your DH and the rest of the family will be enraged with you for triggering this regardless of what she has done.
They have all been trained to do anything and everything to keep her from erupting.
They are terrified of this - this is how she controls and manipulates everyone - always simmering volatility - the threat of a blow out.
Your DH would have seen this from an v early age and it would have been terrifying - so his automatic knee jerk is to comply with her and keep her calm.
This is all about HIS discomfort.
This is evidenced by his comment requesting “it’s easier if you just let it lie” - it’s easier for HIM. Not YOU. Know that.
He is trapped in FOG - scared of anger - so don’t fall into the trap of being the angry wife on the other side - because he will then see himself irrationally “stuck in the middle” because there is no middle when you are married - there are compromises etc.
So he needs to be educated about this toxic engulfing dynamic. That he is part of the enabling but that YOU are not playing tug of war. YOU have dropped the rope.
Underneath / subconsciously he is v scared of his DM - he knows he is being controlled so needs GENTLE support and encouragement to be confident setting boundaries with her. He may need professional counselling for an independent view on this as now he likely sees YOU as the problem because you are asking him to behave differently from his trained gut reaction.
Know that you are right and MIL is wrong but the only person who can shift this dynamic with her is your DH not you.
Maybe one clear talking to him with YOUR boundaries and expectations of HIM as a father and a husband and consequences which you carry out in ACTIONS.
Decide what your weekly routine is as a family FIRST and then schedule time in when he sees his DM and that he doesn’t get to drop his family and go over on short notice.