Your mother is 83 years old is passing green colored stools and green colored vomit as well .The main reasons may be from the following:
a) Eating too much of Broccoli.
b) Medication can also cause this.
c) From food poisoning that is E coli induced.
d) Use of laxatives.
e) Digestion problems
f) Irritable bowel syndrome
g) Iron supplements.
Green stool can be a normal condition or may be a sign of an intestinal disorder. Bile that is yellowish green in color when it is passed through digestive tract it changes its color to brown. However in case of Salmonella infection, it passes as it is. Depending on the reason or cause. I would you to get a set of investigation like complete blood tests, stool routine and culture .You can consult the doctor with these reports for further management. Hope this helps.