I’ve followed this post quite a bit, as feel for you as similar circumstances to what we have had at times with jobs, house, a pre-maternity mortgage, children, 4 days/nursery, no holidays or cars on finance etc with nothing left at end of the month even though we had good jobs - it’s a pinch point, a moment in time when children are small.
If you managed to balance it when taking on a second child and the extra childcare etc that comes with that then it will sort itself out, you’ve just got slightly harsher timing for your pinch point as it’s coming right as cost of living is changing but you are going to benefit from childcare changing as they go to school etc.
I would absolutely stick to your masters, and your 4 days if you can for the sake of sanity and family life whilst they are small. I don’t know how old you youngest is but going to full on for career before youngest is 3 yrs is tough going.
Also would try to stick with your house now, you bought it when prices were lower, unless you are going to default on your mortgage payments you will lose out in the long run if down size now as what you could get is going to cost more for less than it would have and you may never get back to the house you are at now or not at least without it costing you a lot more later on and a higher mortgage to do it. I would choose to eat beans on toast for dinner for the foreseeable than do that.
As lots of posters have said, the key will probably be if you can rejig things for a re-mortgage to help costs that way. If you can that may be enough to help you through this