I think this comes down to two stubborn people having a hard time accepting a middle ground. You are both convinced that your way is the "right" one and that the other person's way is harmful and wrong.
From what you've said this has been a dividing issue throughout your marriage -- your H doesn't like how you parent, his family has accused you of monopolizing the kids. You don't like how he parents, you think he is unsympathetic, abusive and extreme.
It seems obvious that neither of you are going to switch camps on this issue -- I think you're afraid that getting behind H will be abusive and unnecessarily harsh for the kids. H isn't going to get behind you because he thinks you coddle them and allow them to live in a manner that disrespects their parents, so he's going to step away and then hit you with "I told you so" whenever things go wrong.
So you have incompatible parenting philosophies and you're both stubborn -- what are you going to do?
1) You can withdraw and take the "my house, my rules" approach which it doesn't seem like you want for the sake of your kids.
2) You can try to be deferential to H when it suits you, but I think we all have serious concerns about his abusiveness.
3) You can try for a middle ground that you both agree upon.
For #3, I think this has to be in terms of a framework versus a negotiated response to each issue as it arises. I don't think either of you will defer to the other's claims of righteousness, so the very best course of action is probably to take a parenting or co-parenting class together where there is an expert or authority on child rearing who will mediate polar disputes.
What I would suggest is discussing the issue with H: "H, we don't agree on parenting approaches, we're not going to come to agreement on our own, and not doing so will be a continual source of tension. I recommend we seek some outside help to agree on a framework for co-parenting."
What is a framework? I see it as a set of rules:
1) No physical punishment: we will agree not to engage in beating, hair cutting, etc.
2) No verbal berating: we will agree not to use works like "stupid", "dumb", or other words that would undercut our children's self-esteem
3) Negative behavior will have consequences: We will agree on a list of punishments for minor to major infractions, and we will enforce them consistently. We will agree on what constitutes major and minor infractions.
4) We will expect our children to be respectful: These are the behaviors we consider to be disrespectful (list), and these are the types of behaviors we equate with respect (list).
The trick here will be negotiating the punishment schedule to something you are both satisfied with, as well as what constitutes major and minor infractions. This will be a negotiation to be sure, but you shouldn't end that process until you both agree.
If you negotiate that list in advance, and H sees you applying it as agreed, it will probably make everything easier for both of you.
The other benefit is that talking about it as a framework will remove the emotion associated with any given incident.
Accuray
Married 18, Together 20, Now Divorced M: 48, W: 50, D: 18, S: 16, D: 12 Bomb Dropped (EA, D): 7/13/11 Start Reconcile: 8/15/11 Bomb Dropped (EA, D): 5/1/2014 (Divorced) In a New Relationship: 3/2015