Can Roman Catholics fulfill their sunday obligation by attending a Byzantine Catholic Mass and receiving the Eucharist there? TB

TB:  

Yes!  That's the short answer.  

Now for an explanation:  Roman Catholics may "fulfill their Sunday obligation by attending Mass in any Catholic rite ... which is in full communion with the Roman Catholic Church."  The Byzantines are in full communion with us, so yes! Vatican II said this was ok because " ' such individual Churches,whether of the East or of the West, although they differ somewhat among themselves in what are called rites (that is, in liturgy, ecclesiastical discipline, and spiritual heritage), are, nevertheless, equally entrusted to the guidance of the Roman Pontiff, the divinely appointed successor of St. Peter in  supreme governance over the universal Church.  They are consequently of equal dignity, so that none of them is superior to others by reason of rite. They enjoy the same rights and are under the same obligations, even with respect to preaching the Gospel to the whole world (cf. Mk 16:15) under the guidance of the Roman Pontiff.  (Decree on Eastern Catholic Churches, n. 3)."
from Catholic Replies by James J. Drummey  CR Publications, Norwood MA