People can only take advantage of you as much as you allow them to.

You have two choices. Either sit there fuming and feeling you have been taken advantage of or respond to her that this is not your agreement. That you were expecting the children/child for whatever days you were expecting them, that you have planned your availability accordingly.

Once you have done that - one of two things will happen. Either she will back down and keep the agreement in place or she will refuse to back down.

If she sticks to her guns you can then decide if you are going to keep her or give her notice.

I would strongly suggest as a minimum that you communicate the agreement as you believed it to be, and that in order that it doesn't happen again, you put a signed contract in place. If the Mom isn't willing to do that, then give her notice and she can go elsewhere. Don't give her an opportunity to repeat this.

You have said you are in a high demand area and that her plan is for the grandmother to watch her children so you are in the fortunate position of being able to have someone else in her place when school begins after Christmas.