We are not related but I am interested in the names you mention.
You will find that the correct name is (PROPABLY) Mavromichalakis and she was born in Athens.
I am not 100% sure but the -akis was added in Athens. Before that was Mavromichalis. As you know, she has a sister Stella, etc etc. They were not native to Crete.
Assuming the spelling is Mavromichelakis than all the above is wrong, because "Michelis" is Cretan and that makes Mavromichelis (Mavromichelakis) a Cretan name which will be very difficult to trace. (It does not appear in any records).
The other name you mentioned, "Gialitakis" does not appear in any Cretan records. There is a Venetian name "Ialino" that existed in Crete for 300-400 years, and from it we have Gialinas and Gialinakis but not Gialitakis. There is also a name: Dialinas & Dialinakis. Dialinas from d'Ialinas (from d' Ialino).
Where did see the names?
PS: I did reply in one of your older posts, but I did further research since. My comments here are up-to-date.