Don't worry about school years until later. They'll cope with whichever one it is whatever. Especially with each other to bounce off.
I don't mean to be rude, but IMO it's a little frivolous in comparison to what's about to happen.
Take every option you can to make the birth as smooth as possible and minimise as many risks to your wife and children as possible.
Inductions don't always work immediately or as smoothly as some people believe.
We had our first child in January. Wife was induced on a Sunday and spent the next 4 days with contractions rising and dropping , with no sleep, in and out of delivery suites. It left her mentally and physically exhausted by the time she was dilated enough on the Wednesday. The baby became stressed by it all too, and they then needed to go to an emergency caesarian for the birth. They're both doing fine now, but it was no cakewalk.
I'm not saying all inductions go like that, but it's more than people realise. I know of two others from when my wife was in hospital. Complications happen.
If delaying the birth means the kids will be a bit bigger , then the birth may be a little more difficult than it would otherwise have been. It would probably be fine, but if there are other complications, or your wife doesn't react to the induction in the predicted way, then these things can add up. Especially with twins.
You both need to talk to your medical people. As it's your wife's idea then I know you'd have trouble convincing a pregnant mother to change her mind. But make sure she understands any risks she's taking.
Personally, the risk outweighs the reward for me.
The other side to the argument could be that they might come out naturally between the two dates you're looking at, with no induction needed. I'd guess that would be best, but I'm no expert. Speak to your doc's.
Good luck to all of you whatever you decide.