"What is the purpose of the scene in which Oedipus bids farewell to Antigone and Ismene?"
After he blinds himself Oedipus must obey his earlier decree in which he said he would rid Thebes of his father's killer. Since that is himself, Oedipus thus imposes self-exile.
He pities his two daughters Antigone and Ismene most, since they are innocent victims of his murder and incest. They will never find husbands or secure dowries. He knows they are cursed:
As to my children's children still must cling,
For what of infamy is lacking here?
"Their father slew his father, sowed the seed
Where he himself was gendered, and begat
These maidens at the source wherefrom he sprang."
Such are the gibes that men will cast at you.
Who then will wed you? None, I ween, but ye
Must pine, poor maids, in single barrenness.
O Prince, Menoeceus' son, to thee, I turn,
With the it rests to father them, for we
Their natural parents, both of us, are lost.
O leave them not to wander poor, unwed,
Thy kin, nor let them share my low estate.
At first, Oedipus wants both his children/sisters to escort him, but Creon forbids it. Later, we know in Oedipus at Colonus, it will be Antigone who will escort into his final resting place.
So says Enotes:
Oedipus entrusts his two daughters to Creon’s care, saying that with their marriage prospects totally blighted and the career world a men-only place they must be protected. The new ruler promises the broken, blind king that he will take care of the two little girls, Antigone and Ismene. Oedipus says he is less worried about his sons. They will be more able than his daughters to make places in the world for themselves because men have more opportunities, he says.
This scene is bittersweet. Oedipus' blinding shows that he is a just ruler: he punishes himself for not knowing what he should have known. His plea to take his children with him to prevent their suffering and unhappiness also shows his compassion. Indeed, he has become a blind seer, much like Tiresias.