I think you were right the first time about what your H thinks of feminists, but I also get the impression that you were on the same page for a long time....I hope you're not now.
And just because the OW is an assertive (as opposed to bolshy) career woman, it certainly doesn't make her a femininist. I am sceptical incidentally, that this "bolshy" comment of his, would have been made about a male marketing executive.
So what you're saying is that part of your rationale for him coming to the house is to see him yourself and to irritate the OW? That's honest and especially the latter reason, understandable but Solost your goals in this situation right now should be to put the DCs' welfare first and to irritate him. The OW is not your enemy - he is.
Separating couples often agree on weekend parenting for the non-resident parent and it's often a grave mistake. It means that you get to see the children when they are tired and when life has to run by the clock at all times, and your H gets them when they are relaxed and fun/late nights beckon. I also think you might be falling into the trap of thinking that just because one of your DCs says she doesn't want to see where Dad lives, they all feel like that. She might also be sparing your feelings, bless her.
Additionally, I don't think you are projecting far enough ahead and seeing the opportunities of a shared parenting arrangement. Shared parenting means that in the time spent with Dad in this case, he is responsible for everything. At the moment, your H rolls up to a clean house and everything is washed, ironed and ready for the DCs' activities. He doesn't get the shit stuff that gets worse as children get older. The refusals to get out of bed in the morning, the PMT in teenage girls, the gruntiness that is a teenage boy.
Soon, your lad will want to do his own thing with his mates on a Saturday and that's normal and healthy. Being forced to spend a day with his sisters and his Dad, is going to intrude on his normal development.
This current arrangement of whole Saturdays and ad-hoc nights in the week with your home as permanent base is not good for them, or you. The only person it's good for is your H.
If your H lived nearer, he could enter into a proper shared parenting arrangment, having them for part of the school week and you could alternate weekends. This would free you up to realise some of your own ambitions in life.
Now, that might seem a step too far for you at the moment (although lots of families practise this arrangement, including some friends of mine) but perhaps it's something you can work towards?
I think it starts with you using this catalyst of the new job, to agree a new schedule. Explain that Saturdays no longer work for you and won't for much longer, as far as the DCs are concerned (especially DS). That seeing the DCs in the family home is actually upsetting them, one in particular. It's now time to formalise everything; the finances and the time spent with the children.
Ask him to suggest a regular weekday night or nights or a rota of alternate weekends. The first obstacle to this is him living so far away, so it will be his choice if he can't do that and move nearer. But if you take away your house as the base camp, this will press the point home. He will just have to find a way of seeing the DCs and it will be his problem.
However, it does mean you'll have to remove obstacles in the way, such as agreeing to him having the DCs at his home (and by default seeing the OW) but I really think this is going to be something you'll have to swallow if you're putting the DCs' interests first. If they don't want to see her, they can tell him that and then it will be his problem to tell her to make herself scarce for the day, won't it?
In answer to your question about male/female roles incidentally, I think it's often the case that women fall into the arrangements that their own parents had and it works as long as one of the partnership doesn't abuse their greater economic power and the societal expectation that men can up and leave when they want, leaving women with the DCs and no earning power of her own. It also works if the one at home continues to have no other ambitions outside of the family.
Unfortunately, this arrangement has worked against you because your H leaving has left you vulnerable and without many options. Meanwhile he has been allowed to live independently elsewhere, suffer nothing like the approbation a woman would get if she left her DCs for an OM, continue his career, retain a financial interest in an accruing asset (your house), have none of the hard graft involved with raising children, see his DCs in nice surroundings without ever having to take time off from work (except for nice things like concerts).
Nice work if you can get it, eh?