You are not unreasonable here. If you have come from a family where such toxic behaviour like they have pulled here is thankfully unknown, it is very hard to comprehend at all why they behave like this (its because they want absolute power and control). This is also perhaps why you have not been able to let rip at them, perhaps for fear of hurting your DH as well. You likely as well come from an emotionally healthy family unit, your DH has clearly not been so lucky. There is really no reasoning with the crazy and your MILs idea to clear the air with a family dinner was really anything but. They have no intentions at all of "clearing the air". They would have behaved too exactly the same regardless of whom your DH went onto marry.
"Part of my wants to explain to them why I am going LC / to get it off my chest, but part of me thinks to just do it and leave DH to explain".
No do not explain anything to them; you cannot reason with the crazy or dysfunctional. The rules regarding familial interactions really does go out of the window when it comes to dysfunctional and otherwise toxic families. Your DH does not have to explain anything to them either. They do not like you, never have liked you and never will like or accept you. Do not talk to them at all and do not expose your child to them and their emotional manipulations either.
It is not your fault nor your DH's (or even his sister's for that matter) that these people are like this, none of you made them that way. His sister's role as the golden child is also a role not without price either, but she is unaware of this.
People from dysfunctional families end up playing roles; his sister is favoured (the golden child) and he is the scapegoat for all their familial ills. These roles are interchangeable but once applied tend to stick permanently. Such structures are commonly seen in families where the parents are disordered of thinking. Your DH has had a lifetime of conditioning at their hands and he is far, far more afraid of them than he is or ever would be of you. This, along with his own inertia, when it comes to dealing with his parents, is why he is behaving the ways he is. Love is always conditional and not ever freely given in such families.
They have really messed up your now husband and he has little to no boundaries re them at all. He is also mired in fear, obligation and guilt re them and like many adults of such toxic parents still seeks their approval (approval which they will never give him).
Your mistakes here were to move anywhere near them and in particular to at all involve them at all in any aspect of your lives or your property. They really cannot be trusted here and will continue to nose about and poke their noses in where they are not wanted. Do not expose your child further to their emotional manipulations going forward.
Your DH ought to be seeing a BACP registered therapist and one at that who has vast experience in dealing with toxic family units. Its that serious a problem and one that you alone are not going to be able to solve. Coming out of the FOG is going to be a long and painful journey of realisation for him.
No do not explain anything to them, your DH does not have to explain anything to them re you either. You've already stated a boundary, stick to it. If he at all wants to continue what is really a one sided relationship with his parents he can do that but it does not follow that you have to do so.
Have a read of "Toxic Inlaws" by Susan Forward, your DH should read "Toxic Parents" by the same author as a starting point. Do have a look too at the "well we took you to Stately Homes" thread on these Relationships pages and read too the "out of the FOG" website.