Yes compressed hours are plummy, why do you think the OP wants that work schedule oh so badly? It’s because you can get the same salary by working a little longer 4days a week so you get that 5th day off. No matter what your job is, it is always more plummy to work 4 ten hrs days vs 5 eight hour days. I’ve had a compressed schedule and managed employees on compressed schedules. Everyone who could have a compressed schedule wanted it, and everyone on a compressed schedule would fight tooth and nail to keep it.
I don't think its unreasonable to expect a parent to try bloody hard to find employment that allows them 2 days a week to be with their children and give time to their family, are you suggesting the time a parent spends with children has no value?
But finding a job with fewer hours and more pay and crucially no weekend work in a type of job that usually requires weekend work doesn’t depend on how “bloody hard” you try, it literally depends on the plausibility of such a job existing. Most jobs that have weekend work, you can’t opt out no matter how hard you try. If you’re in retail, hospitality, hospital, estate agent/property management, many trades (Plummer, gas engineer, electrician) asking to never work a weekend will result in the sack. So my issue is I don’t think the OP is being realistic about her DH being able to find this unicorn of a job.
So no, I’m not implying a parents time with their children is unimportant, it is important. And in fact, I pointed out the OP is being selfish by prioritising her need to have twice as many days with their DC over her DHs time with their DC. Because it is unlikely the DH will be able bring in the higher salary she wants him to have without working more hours, reducing his time with the DC even further. So that’s why if she wants more money, she should take the job offer she already has for higher pay but a 5 day work week. As then she still has more time with the DC than her DH does, but she’s not risking him having even less time than what he has now.