Just a semantic issue.. Unless you're buying fake juice, juice IS naturally sweetened. Fructose is why fruit is sweet, it's a naturally occurring sugar in fruit. (If we really want to go there, sucrose is why sugar cane is sweet, which is another naturally occurring sugar. The whole 'comes from a little green leaf' stupidity commercials drive me nuts... Because table sugar comes from a grass, as does corn syrup, maple sugar from a tree, insect excretion sugar -honey- from insects, milk sugar from a mammal.... :D)
So if the debate is natural v synthetic... Sucrose (sugar cane), galactose (milk sugar), fructose (fruit sugar).... These are ALL natural sugars. As opposed to synthetic sweeteners (although aspartame is bananas+milk) which are chemical creations, some from nature, some purely chemical.
Different sugars affect the body in different ways as they break them down to make glucose (the only nutrient the brain runs on... Glucose & electricity & oxygen... Although its BUILT almost purely from fats), but sugars in our diet are ESSENTIAL to life, we just eat more of them as a society than we really need to.
Which I suspect is the actual hang up. Too much sugar in your children's diet being the concern?
You can keep up the juice wars... Or turn the problem on its head and lower their sugar intake in other areas... Namely starches (aka, sugar. Starch is just a common usage word for 2-5 sugar combinations, nearly always including glucose).
Pasta, bread, rice, etc... have almost no nutritional value OUTSIDE of the starch content. For the very little that you lose, just add wheat germ to veggies/peanut butter &honey, etc.
Just A. option.
OTW, one of my house rules is that I'd it becomes a fight.. It goes away. (Similarly, if you whine you don't get what you want).
So to ME the deciding factor would be is:
-this a dietary issue? (too much sugar in their diet)
-a behavioral issue? (not taking no for A. answer)
-a marriage issue? (being talked down to, etc)
-------
In my house? Juice, milk, water, soda, tea (hot infusion), fruit in water (cold infusions), decoctions (brought to boil)... We drink them all. Our diet changes fairly regularly, however, so the content is fairly consistent. AKA if we're having potatoes and bread or other starches, we stick with less sugar in other areas. If we're protein loading, no worries on getting sugar from another area. It varies meal by meal and day by day (ex: diet on a sports day looks different than a diet on a reading day).