Can we film a story time done at the library using copyrighted books, and then either stream the event live over Facebook for a one-time showing, or film and upload the story time to our library's YouTube channel? The purpose would be so that patrons who cannot come to the library will still be able to participate in story time and gain early literacy benefits.
This is a lovely idea, but any library considering something like this should get assurance that the work is in the public domain, or have permission from the authorized licensor (who is not always the copyright holder), before filming/streaming.
A great example of a permitted derivative work is a commercially published audiobook. Check out the credits on an audiobook listing—they generally recite two copyrights: the first for the original work (used with permission), and the second for the audio recording. This is how the law both limits and promotes such recording.
A few other legal considerations approach this scenario, but don’t quite apply:
That said, because a live reading could promote the works featured, I imagine there are publishers who would grant a limited license for such an endeavor. However, depending on their contract with the author(s), a publisher might not be able to! In any event, asking permission is a case-by-case exercise.
The good news is that the reading itself, at the physical location of the library, is allowed so long as it meets Section 110 (4) of the Copyright Act (this probably isn’t news to most librarians).
Very often, attorneys are perceived as throwing cold water on project like this, and hopefully this answer has shown why that is usually our only option. That said, if there is ever a specific work a library wants to plan an event around (a specific book, etc), it is worth it to investigate the status and licensing posture of that work. You never know what you’ll find when you check the status, or the ability to get permission, for a specific work.
I wish you all good reading.
 No longer protected by copyright…and for that matter, not affixed with a trademark the owner could claim you infringed.
 Because it technically “makes a copy” as it goes, streaming is often considered duplication. If you ever feel like causing a healthy debate, ask three intellectual property attorneys and a U.S. Supreme Court Justice to comment on this line of case law.
 Per Section 101 of the Copyright Act: A “derivative work” is a work based upon one or more preexisting works, such as a translation, musical arrangement, dramatization, fictionalization, motion picture version, sound recording, art reproduction, abridgment, condensation, or any other form in which a work may be recast, transformed, or adapted. [Emphasis added.]