Don't have it in the house. If the kids want something sweet, they go on a walk with their father and buy it/eat it outside. Might reduce the number of times they have it and they'll learn sweets/ice cream/cake/biscuits aren't compulsory every single day - despite what they learn from school dinners.
It's a lot harder to binge when it's going to involve getting up, getting dressed, going out of the house, finding somewhere open, choosing what you want, waiting at the till, paying for it and then eating it - and the emotions that have largely triggered this urge can dissipate in that period.
However, eating higher protein snacks is very good for curbing cravings for sugar - for some reason, whilst it's possible to eat sweet stuff almost without ever feeling satisfied (albeit all the way up to feeling sick), eggs, cheese, etc, are very good at filling the hole in your feelings that you try to cram with sugar.
You still need carbs, as completely avoiding them can also trigger a binge at the first taste of sweetness - it's a human instinct/response - but carbs like potatoes, rice and fruit, rather than Haribo and Magnums.