does medea use her children as a medium to take revenge upon jason?

Medea is willing to sacrifice everything to make her revenge perfect. She murders her own children, paradoxically, to protect them from the counter-revenge of her enemies; she also kills them to hurt Jason, although in slaying them she is dooming herself to a life of remorse and grief. But part of Medea's appeal is its power as a revenge fantasy; just like Medea, all have at one time or another been beset by enemies whose power is institutionally protected and unfair.

Medea believes that her children should be killed in love rather than hate.... which is why she chooses to do the deed before another....

"I've made up my mind, my friends.

I'll do it—kill my children now, without delay,

and flee this land. I must not hesitate.

That will hand them over to someone else,

to be slaughtered by a hand less loving.

No matter what, the children have to die.

Since that's the case, then I, who gave them life, will kill them."

She also killed them to take revenge on Jason.

"Well, your sons are gone.

That should cause you pain."