What unfortunate things have occured in Antigone's family prior to the death of her brothers?
What do you consider unfortunate? Oedipus and Iocaste (Antigone's parents) might have lived happily ever after, were it not for the unfortunate discovery that they were mother and son. Your question is relevant to the play only in so far as the answer would shed light. In Anouilh's 20th century adaptation, the playwright has Antigone say, "We are of the family that asks questions, and we ask them to the bitter end." This may give some explanation of Antigone's character.
The civil war between Eteocles and Polynices is also part and parcel of Antigone's past; her brothers waged war against each other, and were both slain. Antigone has pledged her life to ensuring that both receive a humane burrial. Is it "unfortunate" that her brothers killed each other? Doubtless. But it is more important to consider the depth of Antigone's committment to her conscience.
One of them is that her father, Oedipus, unknowingly murdered his own father, became king, and married his mother. When Oedipus discovered this, he put out his eyes and wandere'd as an exile from Thebes until his death.