Agreed, not an overreaction. CS was trying to problem solve and she can be given some points for that, but again, making it a done deal and then presenting the solution was thoughtless at best (and unprofessional - I would expect more from a college student). Babysitters/nannies will frequently complain about not being viewed/compensated according to their professional expertise, but if you want to be treated as a professional you have to act like one.
OP was clear on the job requirements. Yes, stuff happens, but sometimes that "stuff" forces us to make adjustments and choices elsewhere. It would not be rude of OP to talk to the neighbors with as little justification as possible. "I am so sorry that CS made this arrangement with you without checking with me. It won't be possible to follow through on this, though I have your daughter's name on my list of potential baby-sitters for the future."
I'm curious how CS got together with Neighbor Daughter to even suggest this. Are Neighbors stalking OP's house, seeing who she has over there watching the baby, knocking on the door, saying hello?