It is best to consult with said Greek Orthodox priest of said fiancee’s Orthodox parish.
Usually, one has to be Orthodox to receive Holy Crowning in an Orthodox Church. However, exceptions have been made, i’ve heard.
Your Bishop would have to give you his dispensations for this. Technically, the children would be Orthodox.
Godparents usually have to be Orthodox.
One might convince one’s Orthodox spouse to receive Holy Crowning in the Ruthenian Church. The Orthodox party would have to agree to this, as well as the Orthodox party’s Bishop (which is extremely unlikely, I hear). The children would then be raised Ruthenian Catholic.
Interestingly enough, Kyr Elias Zoghby+, memory eternal, was from a mixed marriage. His Father was Syrian (Antiochian) Orthodox (a convert from the Maronite Catholic Church) and his Mother was Melkite. He grew up going to both Churches, though I do not know where he was baptized or whether he received Holy Communion in both Churches or only one.
I hope this helps.