Thank you all for your replies. I do agree that Tolkien, unless he had a brilliant poker face which he wore for a few odd decades, probably did not write The Lord of the Rings with the intention of creating a sister for himself.
However, the sister connection is still an interesting one, and I think these three relationships have a lot to say about the whole of Tolkien's literary achievement.
Galadriel plays a relatively small but extremely important role in the Lord of the Rings: through three acts she does her part to save Middle earth: the act of renunciation (refusing the Ring), the act of sacrifice (Nenya ergo Lothlorien), and the act of giving (the gifts which she imparts on the Fellowship, all of which become necessary at some point to complete the Quest).
It is never mentioned that Galadriel is a sister. Nevertheless, we are given access to that knowledge via The Silmarillion.
Arwen is another figure who is central to the plot of The Lord of the Rings: she is Aragorn's earthly - I would even say sexual-reproductive - motivation for fulfilling the Quest. Without her, his ascent to Kingship is a burden without personal reward.
We know in the narrative of The Lord of the Rings that Arwen has brothers, but Elladan and Elrohir play only a passing role in the narrative. All three are mentioned in the Silmarillion, but they play no key role in the narrative.
Eowyn is crucial to the plot of The Lord of the Rings: she slays the chief emissary of Evil on Earth (Sauron). She is rewarded for this moral act with marriage; her brother, meanwhile, plays a less important role, but in the end they are separated. Eomer and Eowyn exist only in the moral framework of The Lord of the Rings: they are not mentioned in The Silmarillion, thus are totally unimportant to its narrative.
If we look at the Silm as Trans-moral and the LotR as Moral, we have this relationship
Galadriel : her four brothers :: Morality : Trans-morality
Eowyn : her brother :: Morality : Unity
Arwen : her two brothers :: The bridge between trans-morality and morality : Eternal Duality
The logical conclusion is that wrong acts can exist in Middle-earth, but cannot exist in the Silmarillion.