Sometimes my mother, who has Alzheimer’s, “refuses care” — i.e. she does not allow the caregiver to come in, and basically shuts the door in her face.
In general this is the exception to the rule and not the norm, but it does happen.
Under these circumstances, am I required to pay the caregiver for the time she had expected to work?
The general rule is that one would have to pay for the time she expected to work, because having set aside the time for working with your mother, this is now “lost time,” that she won’t be able to make up.
According to the strict halachah, the obligation to pay is possibly less than the full amount (sechar batalah), depending on the circumstances (the type of work, and how much the worker will be prepared to lose from his income in exchange for not working).
However, I believe that the general custom today is to pay the full amount, and in that case, you should pay the full sum for the lost hours.