Shared email address (parent/child)
Parent's emails should be visible from the child's "Relationships" tab without actually clicking through to the parent.
Alternatively, the Relationship Block extension allows you to put the parent's info on the summary screen.  Not ideal, but it saves you a click.


After that, I think you're looking at commissioning an extension, or a modification to an existing one.  It probably wouldn't be hard to include a clickable email address via the Relationship Block extension.  Doing a "shared email" extension is pretty doable these days also, due to some under-the-hood improvements in CiviCRM 5.