I agree with the earlier comment that Euripides' shaping of the character of Glauce is rather non-existent. The only glimpse we get of Glauce's character comes at around line 1135ff, when she accepts the gifts of clothing from Jason's children (Medea has laced the gifts with poison so that when Creon's daughter puts them on she will be killed).
Once Glauce sees the gifts, then she seems to be cast by Euripides as a stereotyped woman who can be won over by lovely trinkets. She immediately puts aside her disdain for Jason's sons, accepts the gifts, and soon puts on the deadly clothing. Euripides' description of Glauce sitting at a mirror and admiring herself would seem to point toward her vanity.
In contrast to the other commentator, I would say, though, that Glauce would not have had any choice in the matter of who her husband was. In ancient Greek society, marriages were arranged by men and the woman would have had no choice in the matter.
In Medea, the character of Glauce is rather flat and almost stereotypical. Jason marries Glauce for her status and wealth; as the daughter of Creon, Glauce provides Jason with opportunities for advancement within Corinth. Although she is technically Jason's second wife, she insists that she be revered. She allows Medea to stay around only to appease Jason's love for his sons. Glauce does not like Jason's sons, and when they bring her the poisoned gifts, she snubs them before being taken in by her own greed. The reader never learns much more about Glauce, and it is unclear why she accepted Jason as a suitor even though he was married already. So Glauce remains a flat character representative of greed and wealth in the play.