In Twelfth Night, there are no nuclear families intact.
- No fathers; both are deceased.
We know that Olivia’s father (“a count” [I.ii.36]) had died some “twelvemonth since” (I.ii.37).
We don’t know how long ago Sebastian of Messaline died, but we do know how old the twins (“both born in an hour” [II.i.18]) were when he died: “That day that made (Viola) thirteen years” (V.i.243). And when revealing their identity, they both use their father to legitimize their claim (Sebastian in Act Two, Scene One, and Viola in Act Five, Scene One). - No mothers; one is mentioned, but neither appears and both are assumed to be dead.
Only the twins’ mother is mentioned: once by Sebastian to explain why he cries so easily (he is “so yet near the manners of [his] mother” [II.i.37]), and once–obliquely–by Malvolio to describe the youthful, almost girlish, appearance of Cesario/Viola (“One would think his mother’s milk were scarce out of him” [I.v.155-6]). - Siblings are missing, either assumed or really dead.
Olivia’s brother died “shortly” (I.ii.39) after her father, and it is his death for which Olivia “hath adjured the sight // And company of men” (I.ii.40-1) for the next “seven years” (I.i.27)
Both Viola and Sebastian believe the other is dead, drowned in the shipwreck that brought them to Illyria.
We know nothing of Orsino’s family, nor do we need to: he is the Duke, and that stature eliminates any other need of identity, personal or familial.
You would think the same of Olivia, as she is now a “countess” (V.i.94), but this is not the case. Or is, in this case, the need of Olivia for deceased family ties, the Macguffin that begins the play: Olivia won’t see suitors because of her mourning (so she’ll see neither the Duke nor Viola seeking a kindred spirit), but the minute she does see Viola–now disguised as the young man Cesario on behalf of Orsino–she falls in love with him/her.