I agree with the comments from the previous person - you do need to develop the character of Glauce in this dialogue. If you look again at the Messenger's speech about the lead up to her horrible death, Glauce can be seen as a generous girl who reacts spontaneously to Jason's children and who is delighted by their gift. She can also be seen as vain and foolish in her eagerness to wear the poisoned robe. You decide how you might convey these aspects of her character. You also want to keep within the cultural context of Greek tragedy so there would be no "baptism" - instead maybe prayers and animal sacrifice at the temple of Hera (goddess of childbirth) or Aphrodite (?). Remember too that Medea is a barbarian and does not have the same status as "a real princess" like Glauce and this understanding of her own superiority may also be an element in her apparent sympathy for Medea's position. Glauce may also be likely to understand and accept Jason's/Athenian rules about women's lives (rather than complaining about them as Medea does at the start of the play). She has the security of being in her own city (Corinth), with the support of her father Creon and the knowledge of the expectations of her society.
As for the Statement of Intention you should be prepared to comment on your use of form, language, audience, purpose and context - you are choosing to write an extra scene in the style of the original text, your language choice is intended to be consistent with Euripides presentation of these characters from Greek myth, you want your audience to witness the confrontation between these two women, Your purpose is to reveal the character of Glauce in more detail and to explore the social context of women's status from the point of view of an "insider" and this would contrast with the "outsiders" view expressed by Medea in the original text.