Much simpler answer; send the kids as UMs, and go on a different flight, or even the same one (without telling them). They get looked after much better by a succession of pleasant staff, and you have a peaceful trip.
And if they lose them you get paid enormous compensation, whereas if you lose them you are hurled into chokey by the Police for negligence.
Failing that, book yourselves and the wife into economy and the kids into Business. They get looked after better that way round.
Edit: Sorry, just noticed you have an infant. Keep that with you, with copious Calpol...you'll have to buy that airside, of course. Unless you can persuade the other one to look after the infant in Business. The cabin staff will help out. (Tip; don't go Ryanair or Easyjet).