So many things make this a completely grey case, the likes of which must frustrate judges, as there is no good solution.
It contains the classic problem in any situation where the parents have wildly different incomes. The kids want to be in the home with the most money, which means all the CS goes to that home, and then the other parent has even less money in their home. So then the kids really don't want to be there, etc. in the vicious circle.
The low income mom's second marriage is breaking down. So that's even less money in her household. No wonder she's desperate for CS even when she doesn't have the kids. Without it, she probably can't even afford a home big enough to accommodate them anymore. No, it's not the responsibility of her first ex to support her because she now has a second ex; I'm just saying this explains where her sudden desperation comes from, and understanding motivation is a big help. Maybe this woman should have figured out how to support herself better by now, retrained for a career she can do despite her disability, invested her equalization, or something other than expecting CS to be SS.
Then, there is the issue of huge s7 expenses, such as the private school fees in this case, which I believe they have done backwards. Deciding what s7 expenses to take on should be done on the basis of your current financial situation. I don't think it's right of this guy to say let's enroll them in private school, so now they live with me due my house being nearest to the school, so now I don't need to pay CS so I can afford the fees. I think it would have been more appropriate to say the situation is shared access, which involves lots of CS, so private school is not affordable on top of that, and then looked into changing shared access before enrolling them. But that's nothing a judge can do anything about now.
This is a case that confirms my belief that CS should be on more of a sliding scale. If she gets them EoW, which is about 20% access, she should get 20% of the combined CS between them. A little money would flow from him to her, not enough to make a hardship for him, but enough to make a big difference in her being able to accommodate the kids for her access time, and let her be able to afford her tiny share of s7 expenses. I guess the judge has tried to approximate this by not having her pay CS or s7 at all, but I think it's like trying to right a wrong with another wrong.
Lastly, the mother definitely has some issues, both with her income earning ability and her parenting ability. But to say that teenagers shouldn't live with her because she doesn't help them enough with breakfast or lunch or homework is a bit silly. They are old enough to be expected to manage that themselves. These children are growing up with an attitude of entitlement which won't be helped by living with dad. It doesn't sound like he's encouraging them to maintain their relationship with her.
Incidentally, this also opened my eyes to the mistaken impressions lower income people have of higher income people. This guy pays a LOT of tax! We may all look at a $300k income and think 'wow, he can afford anything' but it doesn't give the same proportion of disposable income we have at lower levels.
ETA - it's not a gendered problem. This situation could just as easily happen to a high-powered woman executive and a disabled ex-husband.