Hey Brian, thanks for reaching out!
Great question. There are certainly RSS-to-WordPress plugins out there that will convert the entries from RSS to WordPress posts. However, I am not familiar with one that specifically works with custom post types, which is what events are.
Right out of the box, The Events Calendar will import events from a CSV file. If your parent site has the ability to generate a CSV export of events, then that would be an easy way to go.
If the parent site does not export a CSV file, but an XML one instead, then it might be possible to use the built-in WordPress Importer.
Lastly, we do have an extension called iCal Importer that can be used to import events from a valid iCal URL into The Events Calendar. If your parent site has an iCal URL, then this should allow you to import the events programmatically.
Those are the three methods that The Events Calendar can be used to import events from other calendars. Will either of them work for you? Please let me know. 🙂
Cheers,
Geoff