If your partner is very good at their job, and is in a field where being very good is important, you could try the technique used by Bill Mason to get the entire summer off (so he could canoe) every year, while holding jobs (graphic design I think) that typically gave two weeks a year, maybe 3 of vacation:
quit your job (with as much notice as you want to) at the start of the time you want off. When you return from it, apply to various places including your old employer.
The risk is that no-one will hire you afterwards. That's why you need to be good, and being good needs to matter. This is perhaps too extreme a thing to get two or three days off, but if you'd like several weeks to go away somewhere for the holidays, it might work.
I can see your employer's point in not allowing time beyond the statutory days, if your partner is in a field where it's busier at that time, and competition for the time off could cause tensions among the staff. Perhaps asking for a "leave of absence" would also be a strategy.