Should one abandon visiting the mother's grave due to the long distance and hardship, or should one persist in visiting it out of dutifulness to her?

There is no harm in avoiding burdensome travel to visit the mother's grave, because burdensome travel to visit graves falls under the prohibited "setting out" (شد الرحال) except for the three mosques. It is advised to frequently supplicate, seek forgiveness, give charity, perform Hajj, and Umrah on her behalf.