Hey Phil,
Thanks for getting in touch. Sounds like a cool project!
There isn’t a built in way for two websites to directly share events as you’re describing, either in the core calendar plugin or with PRO. However, you can export events to iCal files, and we have an iCal Importer plugin. You could have the other site export events and then import them into your calendar. Might that work for you? Your site wouldn’t need to be running PRO, only The Events Calendar and iCal Importer (so you’d still only need to purchase one license).
Best,
Leah