We have gone low sugar for similar reasons. I don't limit fruit at all but stopped buying biscuits etc and stopped baking. There is one brand of muesli bar that I still buy that they really like and is the lowest sugar I can find.

They nagged for biscuits for a bit, but I just kept saying I forgot when I did the shopping and they would have to remind me on shopping day - then I would 'forget' again. They don't ask now.

For snacks they have fruit, cheese and crackers, kruskits, popcorn, raisins, canned fruit.

I am not fanatical about it and they eat junk at parties and had a bit with the lead up to Christmas but our day to day life doesn't include much sugar. I have some ice creams that are like mini paddle pops that they might have as a really special treat when it is hot. We get ice creams sometimes when we are out but I always get the baby size so there is only a couple of tablespoons of actual ice cream and they still consider that they have had a treat.

For breakfast mine have toast or weet-bix. I put half a teaspoon of raw sugar on it.

Lunch box is a sandwich, a yoghurt, an apple/banana/orange, muesli bar, raisins, chippies, and a fruit salad/another piece of fruit.

So basically we cut out the unnecessary extras like biscuits and baking and have smaller portions of the treats we do have.