[stumped]

what do you mean by " their freeware thing" ?
inside of a Child profile setup with the Freetime app. all sideloaded content is blocked ( books, videos...),
amazon help confirms that is by design, not by accident.
You must be referring to the Curated Kids time Unlimited subscriptions service. that has many more books and videos but it is a monthly fee.
So if you'd bought HP from pottermore , you could not add those versions to a Child profile. In that plan, Amazon are choosing the books, based on the child age you tell them at setup; you still cannot add one you bought elsewhere. So for a child whose reading age is way ahead of actual age, you'd need to lie about their age, I guess.

We do use your child's profile to provide a customized experience in Amazon FreeTime. In setting up your child's profile, we ask you to provide the child's screen name (which can be any word you choose), gender and birthdate,

another by design issue if that within Unlimited, for a age <8 profile, the Tablet is locked to portrait mode, that is a stupid design decision for videos, and even for some kids books. we can use landscape in the simple Free time child profile OK

Enter your child's name, birthdate, and gender, and then select:
Use Amazon FreeTime - For children ages eight and younger, this profile type locks the tablet to portrait orientation - perfect for picture books and educational content.

a final annoyance was that after creating the child profile on the HD, my own not for child HDX demanded that I add a lock screen PIN in front of a profile selection to that device
i.e.because profiles are per account, not per device, they impact other devices n the same account. My e-ink kindle was not affected, but with the HDX I had to create a lock screen PIN then go it and choose the adult profile , then hide the child profile at device level, then remove the new PIN to get it back to how it was.