Hi Kat
While Adriana gets back to her house from Yialos, I can help out:
Dodecanese Seaways only operate to Datca on Saturdays, which is market day there, and the whole purpose is to provide a day return facility. The ferry sets off from Rhodes at 09:10, arrives Symi at 10:00, leaves again for Datca at 10:30, getting there at 11:00.
On the way back it leaves Datca at 15:00, gets to Symi at 15:30, and leaves again for Rhodes at 16:30.