Is it obligatory to fast in expiation for the deceased mother who was in the other car and was affected by the accident she caused?

If the mother is still alive and suffering from the effects of the accident, then no expiation is required of you. However, if the mother died due to the accident, then expiation is required of you. And whoever dies due to an accidental transgression, either immediately or after a period of time due to that transgression, then the blood money is incumbent upon the Aqilah (male relatives on the father's side) of the transgressor, and expiation is incumbent upon the transgressor.