Wow what a *****!!!
I don't think you are overreacting at all. I think it's quite unprofessional of her.
Is there management above her that you can speak with?
Financially speaking... will DD be going into daycare or family taking care of her? For us, if I were to go back to work by the time I pay for daycare and then lose FTB it's hardly worth it. For the few measly dollars extra I would rather the time with my DS and live scarcely for a while, IYKWIM. That said I don't know your job situation, I'm a just thinking out loud