In Kythira, in late November, around the time of Saint Catherine’s Day, you certainly won’t find any "high party noisy place."
In fact, you wouldn’t find that even in the middle of August; it’s simply not the kind of place Kythira is. (For context, I spent a week on the island 3 years ago , we traveled there from Athènes via the Peloponnese, taking a ferry from the port of Neapoli with a rental car, but that would take far too much time for your trip.
Since you only have one week, the best option is to take a flight from Athens to Kythira with Aegean-Olympic or Sky Express. Note that there may not be daily flights in November.
Your mother’s family might have Australian roots, as there was a massive exodus from Kythira to Australia during the 20th century.
You might find this site interesting:
https://www.kythera-family.net/index.php/en
The general tourism website:
https://visitkythera.com/
You will need a car on Kythira, bus service is extremely limited (if not non-existent in November), and the island is quite large.
Therefore, I suggest checking flight availability to Kythira first. Flights generally depart in the late morning or early afternoon. This might mean spending your first night in Athens if you cannot catch a connecting flight upon your arrival in Greece.
Athens is packed with historical sites, but as for how you could easily see historical sites and travel to Kythira within a single week, I don’t really see how that’s reasonably possible. You would have to limit your stay in Kythira to a maximum of 3 nights, which amounts to only two full days. Whether that’s enough for a return to your family roots, that’s for you to decide.