I think its okay in small amounts, but I wouldnt make a habit of it. The sugar content is pretty high, and I def wouldn't switch to the sugar free kind. I think the alternative sweeteners are can be pretty bad for digestion because they aren't a natural form of sweetener. I know personally for myself, anytime I try to drink a diet drink with artificial sweeteners, etc it gives me a stomach ache. Every time.
Having said all that, I think giving her some right now to help with the constipation is okay, especially if she isn't drinking much else right now. You can always try to switch back to plain water, diluted juices after the constipation passes.
Have you tried making your own flavored waters? You can just cut up some fruits and place in a pitcher to steep with the water, naturally flavoring it. see if she likes that
Im the same with sweetners, I cant drink any diet drinks as they give me really bad stomach ache