Is there anything religiously incumbent upon me due to the death of my mother, who fell from my car and was run over by another car, leading to her demise?

If you were driving at a reasonable speed and could not avoid the pothole safely, then there is no blame on you, as you are not the cause. However, if you were driving at an excessive speed that made it impossible to control the car, or if you could have avoided the pothole safely but did not, then you are the cause of the accident.

If you were the cause of the accident, and there was another direct party, who is the owner of the car that hit you, then the liability falls on the direct party (the owner of the other car) if he could have avoided the collision but failed to do so. Otherwise, the liability is on you. The rule is that liability falls on the direct party unless it is impossible to hold him liable, or if the one who caused it was the aggressor. Liability includes expiation (kaffarah) and blood money (diyah), and the diyah is waived if the family of the deceased pardons it.