Having 4 kids of my own I think you may want to approach this from an additional angle. What genre of music does SHE primarily listen to pop electronica R&B rock accoustic? Many believe ESS or AKM will sound bright or warm below 1K that is for the most part true. Here’s the thing you are giving her a tube intergrated (not knowing what it is) I will assume it has a warmish presentation coupled with an AKM dac could be too warm especailly if she likes pop or electronic music.
You mentioned something in your post that goes to the heart of what is really the case with young folk today...they listen to music via their phones; as much as we may want to introduce them to our way of listening they are gonna do as they are gonna do. She may very well get more use out of a Dragonfly Cobalt (and would absolutely appreciate the elevated presentation). With a tube intergrated I’d consider an ESS dac to pull out the dynamics bass and detail something like the Topping E50. A Schiit Modi multibit 2 is a good middle of the spectrum choice both are still bargains and great dacs. You could give her a dragonfly and add a Modi or E50 and be under $500. I’d take baby steps here..