Finishing `Umrah without completing Tawaf

Q: I, as well as my father, mother and brother, performed `Umrah (lesser pilgrimage) during Ramadan about fourteen years ago. When we made Tawaf (circumambulation of the Ka`bah) , and made three rounds, my brother said we had completed Tawaf (circumambulation of the Ka`bah), but my father and I said there were still four rounds left; after which, we returned home. It is worth mentioning that we had made only three rounds of Tawaf around the Ka`bah and completed the rites of `Umrah by drinking from Zamzam and making Sa`y (going between Safa and Marwah during Hajj and `Umrah). We then returned home. We would be grateful if you would give us the ruling on such practice. Should we offer Fidyah (ransom) or anything else in this respect? It is worth mentioning that both my father and my mother are dead, and my brother and I are still alive. Is the `Umrah we performed valid or incomplete? We would be grateful if you could show us what we need to do and what is incumbent upon my deceased parents. Do we have to perform this `Umrah again for which we assumed the state of Ihram (the ritual state for Hajj or `Umrah) only once, or must each of us return and assume the state of Ihram again? I would like to inform you that we live far away from Al-Haram (the Sacred Mosque in Makkah) and are busy all the time. If it is obligatory upon us to offer Fidyah, is it permissible for us to give it to Al-Rajihy Bank located in Sarat `Ubaydah to deliver it to the Islamic Bank to offer the Fidyah on our behalf as is the case with the Fidyah offered during Hajj; or do we have to go to Al-Haram and slaughter the Fidyah? Give us the ruling on this question in detail, may Allah reward you with the best!