The headmistress did not make the rules, but she has to apply them, like it or not.
I once had quite the opposite situation to the one described in the OP. It was before school holidays were published online. My eldest had just started school and they sent home a printed sheet of the holiday dates. Unknown to us at the time, they had published the wrong week for their October half term. We booked to go away for the week they had published, and we paid. A couple of weeks later they sent home a correction. I spoke to them about it, had our booking confirmation and also their original written letter on which we had based our booking. The headmistress acknowledged their mistake, and that I would be unable to get my money back for the holiday by now, and I had no problem getting the holiday authorised.
It is different for you, OP. The rules are much tighter these days.
Take the holiday, but pay the fine if one is applied (or perhaps grandad will agree to help out there). Don't let it happen again.
Don't worry about it affecting their entire school career. That is bollocks. It won't. Year 2 is teacher assessment. Even if they are not in school on the appointed day, they have an otherwise good attendance record. Their teachers know enough about them and their abilities to be able to place them properly when they move on to the juniors, with or without the SATS results.
Stop any suggestion that you would like teachers to cut into their own precious free time and holiday to facilitate SATS for your children though. I would apologise for that suggestion, although my guess is that you were under pressure from all sides at the time and were clutching at straws without thinking of the consequences for the teachers themselves. They do not get paid overtime. Just remember that.
Ensure that this is a one-off (and tell grandad so too, but tactfully), pay the fine if you get it and go with a clear conscience.