Is a son's failure to travel to see his sick mother considered a dereliction of duty, given that there are others to care for her, and that he remains with his family, who have no provider other than him?

If your mother has someone to serve and care for her, and you are responsible for her expenses, then you are not obliged to travel to her, especially since there is hardship in your travel and leaving your family. However, if you can travel without difficulty, you should do so, because a mother often yearns to see her children, especially with severe illness that is feared to be her death sickness.