I'm not sure it has anything to do with. DreamBox itself.
It took me a while to figure out how you got that screenshot. Turns out it's the app switcher view, only you don't have any older apps to switch to, just the home screen. When I look at my multitask switcher it occationally shows an app at the bottom like that; usually FaceBook. I believe this is iOS's guess as to which app you're most likely to want next, since you can tap on it to go straight to that app.
As for the phrase, it probably has to do with how your child's profile is set up. There's is a good chance that DreamBox calls all young ladies Princess. If you find it offensive you should probalby talk to your schools IT admin, and see if they have an option to change it.