Can a girl choose not to marry and dedicate her life to caring for her ill mother, and what is the ruling of Islamic law on that?

The ruling on marriage varies according to the situation. If it is possible to combine marriage with caring for the mother, then that is preferable. Otherwise, there is no sin in refraining from marriage if there is no fear of temptation and if one does not yearn for it. It is advisable not to reject a religious suitor of good character, while it is possible to stipulate the continuation of caring for the mother, either by her living with the couple or by the couple living in the mother's house.