The children are their mother's power in a very real sense. When Medea must appeal to the best intentions of Creon, she presents the case of her poor unfortunate children that are no deserving of any punishment. It is through his pity for the children that Medea is able to remain for a time long enough to fulfill her plans to get revenge. Again, her children assist her when no one else could by taking the poisoned gifts to their step mother. Because the children are innocent, no one would suspect any foul play, unlike if Medea herself delivered these items. Many times all of Medea's plans are built on the assistance that her children will provide for her, and they offer their services to her without any hesitation. She has complete power over them because she is their mother, and at the same time they are able to provide her with a grand amount of help. Medea has allowed her wrath to overcome all other thoughts that she may have. "Immoderate love gives way to immoderate hate...

Additionally, the children have been the key to Medea's success in everything she does. They are powerless to save themselves from her wrath, despite being the only reason she was able to succeed in all else. This betrayal of innocence, trust, and loyal service is what makes the killing of Medea's children the most terrible event in the play.
Works Cited

Euripides. Medea. Trans. Ian Johnson. http://www.mala.bc.ca/~johnstoi/euripides/medea.htm

Geetanjali. "Feminist Reading of Euripides' Medea." Literary Mosaic II. 1 April 2004. http://literarymosaicii.blogspot.com/2004/04/feminist-reading-of-euripides-medea.html

Tagle, Steven. "The Dramatic Appeal of Human Props in Greek Drama." Stanford University. 9 March 2004. http://www.stanford.edu/~stagle/ESSAYS/WIN%20IHUM33A%20E02%20HumanProp.htm