When one thinks of Sophocles' Oedipus Rex (the Greek title is Oedipus Tyrannos), one usually hears questions raised about Oedipus' pride. This question, however, wonders about the pride of Oedipus' mother/wife, Jocasta (also spelled Iocasta).
I would say that it is somewhat mistaken to talk of Jocasta as a person having pride. At one point late in the play, Oedipus thinks that it is possible that he will be discovered as being the child of parents who lack nobility. Jocasta, who at this point now realizes that Oedipus is about to discover his true identity, begs Oedipus to end his investigation.
Oedipus presses on, however, and he thinks that Jocasta does not want him to inquire further into the matter because Jocasta is worried that Oedipus will find out that his real parents were slaves. Oedipus tells Jocasta that even if he is found out to be of humble origin, "you will still have your noble lineage" (Ian Johnston translation). Twice, between lines 1070 and 1080, Oedipus suggests that Jocasta's concerns are due to the pride in her noble heritage.
Oedipus' assessment of Jocasta's pride is mistaken, however. It is not her pride, per se, about which Jocasta is worried, but rather the fear that Oedipus will find out his true identity. Once Jocasta realizes that Oedipus is on the verge of discovering his true identity, Jocasta rushes out and hangs herself.
Some sense of pride may be at work here, as Jocasta cannot allow herself to live to witness Oedipus' discovery of the truth; but pride is not an issue that Sophocles highlights with respect to Jocasta, except the mistaken pride that Oedipus imagines she has when she begs him to stop trying to find out who he really is.