At the very least, go and look at the schools on offer. Private and state.
Locally, we are lucky enough to have several decent state secondary schools. We also have some outstanding private schools. And a couple of not so good private schools.
If I could get my child into one of the excellent private schools, I would take that chance tomorrow. Outstanding education, amazing pastoral care, and I've seen how much they can offer all their pupils, lots of SEN support as well as opportunities for high achievers which just can't happen in the state schools locally.
But if I were offered the chance for them to go to one of the less good private schools, I would only consider it if we'd tried state and been miserable. Because academically, the state options locally are fine, possibly better than this one.
It's all academic; I don't have anyone able to pay for us and the scholarships are long gone now.
I went to state school, and went to university too. So did most of my friends. But we were a minority in our state school. Our careers education was set up on the assumption that pupils would leave as early as possible. University advice was rubbish, frankly (so poor that my parents did somehow manage to scrape together funds to get my younger siblings into private school for a levels).
Go and look at all of the options. Consider whether your children would be better off in single sex or coed schools. If you did send them private, you wouldn't be slating the local schools, but you might just be giving them the opportunity to excel, rather than to do ok.
Or you might not; horses for courses and all that.
You'd have higher costs for uniform (probably) and extra curricular activities in private school. Would gps pay these or could you rise to them? They might well be offset by the fact that shorter terms would mean you'd be able to take cheaper holidays by going at the start or end of your holidays, when state schools still sitting.
You almost certainly wouldn't be the only family where grandparents are paying; it's pretty common these days.
I'd take the offer in a flash myself, but then I only know people it's worked for.
Fwiw if you are worried about control, and if your in laws are seriously loaded, I do know a couple of families who have had the money set aside and put into educational trusts, paying school fees and helping with university stuff, would that feel more secure than relying on them year by year? I suspect there are tax advantages to doing it that way too...