I think it is important to come up with rules that children can understand and preferably see their parents following too. Your fractional sweets during lunch rule seem to be such a rule. Though I'd like to hear what your kids think and say about it.   

And I think it is reasonable to refer to official guidelines instead of making up rules on the spot. Children can understand arguments like "some people got together and figured out how much sugar is bad." Esp. if you can answer their follow-up questions from the guidelines book. 

I have long had an interest in child food consumption. It has turned out to be complicated. What makes it complicated? Metabolism varies heavily different and changes over time. There is an effect on weight, general health, and tooth health. I buy the tooth health aspect - though that depends less on the amount but the type of sweets. But the effects of sugar on general health are not as clear as the recommendations make it sound. 

In practice advice - to parents - the rule is simplified to: "no sugar" or "as little as possible." Or in the USDA recommendations: "less than 10% carbohydrates from added sugars." Which is better but is it a good rule?

If you are an average American, I guess the answer is yes. But there are fewer average people than you would think. Healthy sugar intake can probably vary by a factor of 10 between people (think of the Hadza). The health effect of sugar intake is not even known according to the scientific evaluation of the USDA: 

Conclusion Statements and Grades
* Limited evidence from prospective cohort studies that were based primarily on sugar-sweetened
beverages suggests that higher consumption of added sugars in adulthood is associated with
increased risk of cardiovascular disease mortality. 
* Insufficient evidence is available to determine the relationship between added sugars
consumption and risk of cardiovascular disease in children. 
* Insufficient evidence is available to determine the relationship between added sugars intake in
adulthood and cardiovascular disease risk profile. 
* Insufficient evidence is available to determine the relationship between added sugars intake in
adulthood and risk of stroke. 
* Insufficient evidence is available to determine the relationship between added sugars intake in
adulthood and incident ischemic cardiovascular disease events. Grade: Grade Not Assignable
* Insufficient evidence is available to determine the relationship between added sugars intake in
adulthood and risk of peripheral artery disease. 
* Insufficient evidence is available to determine the relationship between added sugars intake in
adulthood and risk of heart failure. 

-- page 13 in PART D. CHAPTER 12: ADDED SUGARS of the Topics and Questions for Review by the USDA Committee on Added Sugars. 

You have to wonder where the "less than ten percent" recommendation is coming from. It appears to result from dividing study participants into groups with more or less than ten percent sugar intake. And those with less did better. Maybe there is more to it, but it is not clear from the report—no distributions of outcomes, not even confidence intervals. 

I admit that I am biased: I eat a lot of sugar (mostly from sweets; 100g /day) and am slim and healthy (according to my doctor). It has to run in the family. My mother and grandmother are also slim, and specifically, my grandmother (94 years old) loves sweets. I'm not saying that it is healthy in general. I'm not even saying that it is good for me specifically (maybe I would be even more fit if I ate fewer sweets). You can't rule out that there is a wide range of working diets, including ones with more than 10% sugar. And we need a way for Calibrating Adequate Food Consumption.

What works best is if there are just no sweets (that the kids like) at home. You can't eat what isn't there. Another trick is putting a price tag on the sweets. It turns out that they often value their pocket money higher than some sweets - especially if the home price is twice the shop price. 

Children love sugar, and limiting sugar consumption is a common topic in parenting [citation needed]. Besides weight, general health, and tooth health, there is a fourth topic implicitly: Stress from parent-child conflict on this topic. Whatever rule you come up with, that aspect also has to be taken into account.