Why would he have had a problem with the feminist politics Solost?
You see, I find this fascinating. We still live in a society where the vast majority of primary carers are women. While I agree that lots of men would prefer to share the burden of paid work or become the primary carers, your H has never come across to me through these pages, as one of them.
I also think these things are easy to say when he knew that's not what you wanted and still have this sense that if it had compelled him to make a fair few personal sacrifices so that you could retrain, he wouldn't have been at all comfortable with you out-earning him or gaining greater status than him, in the workplace. If you had, I suspect he would have referred to you as "bolshy" just like he did the OW, because these terms are often used by men about career women and are a put-down that they would never attribute to men.
As it was, because you were doing both what he truly wanted and accorded with his view of male and female roles - and you wanted the same, there was no need to manipulate you and no reason for discord. I think if he had truly wanted to be a SAHP, he would have manipulated you for all he was worth.
I think it's interesting how your H was the golden child and his brother, the family scapegoat. That was also the impression I had, without you ever having told us that. Both roles are difficult and confining in families, but the golden child will very often play up to that role and reinforce the scapegoat's fecklessness, to keep basking in his parents' approval. And in later adulthood, this role can become so tiresome that the golden child rebels, or in some cases it isn't as accentuated as before and the golden child misses the attention. I wonder whether there is any coincidence of timing between his brother settling down and finally gaining family approval - and your H's attention-seeking rebellion?
I think it is interesting that you felt you under-achieved and agree that this is a wonderful opportunity to achieve your potential now. Again, I wonder whether this willingness to play a supporting role and lack of ambition were traits that your H found very desirable, in the bigger story of Him?
Regarding the DCs, something needs to change here Solost and fast. He certainly should do his share of childcare, but not in your home. I think you're either going to have to get the DCs cared for by others while you work or drop them at your PILs and let your H care for them there, like I suggested yonks ago. It's his choice to live 100 miles away and he's trading on that, in this situation. Ideally, whatever arrangements you make should achieve two objectives: that he stops coming to your home full stop and secondly, that you don't see him.
How do you feel about not seeing him? How much of this is still about your need, as opposed to your DCs? How much of this is about you being soft with him and pandering to his needs, rather than the DCs?
The DCs might well want to see him, but I bet they don't care where that is. What is indisputable is that this situation is confusing for them and is causing your oldest DD especially, more upset.
There is of course another suggestion that I would understand you resisting, but give it some thought.
It's pretty evident that despite what your H says, this relationship with the OW is here to stay and there are no outward signs of it dissolving. You seem pretty sure that your H doesn't want her to meet the DCs now, but have you thought of calling his bluff again? Suggesting he moves with her nearer to the DCs so that he can take the kids to see his new home (and by default, meet her)? And has the DCs there in future? As a general rule, separating parents are encouraged to let the DCs see their new environments anyway, but your DCs have never seen where he lives and spends so much of his time.
If you consider all these options and can be sure that you are putting the DCs first and not you or him, I think you will achieve what's best for them. The current situation was never best for the DCs and was never best for you. It suits him though.
I also think you will completely wrong-foot him with these changes and it will be such a clear sign to him that you have moved on and have detached from him. But please, please do it for the DCs Solost because this situation is damaging them.