This is not likely life threatening, as your sister's dog is showing signs of colitis
, inflammation of the large bowel. Colitis is commonly the result of dietary indiscretion, but can also be caused by sudden change of food, parasites, infections, and even stress. I generally will run a stool sample to rule out parasites, treat for parasites if found, and if none are found, treat with an antibiotic called metronidazole for one week. In most cases, metronidazole will clear up the colitis, resolve the blood, mucus, and loose stool.
I cannot be certain what shot your sister's vet gave the dog, but since colitis commonly causes an increased urge to go which commonly results in accidents in the home, I will commonly give an injection of atropine to help reduce colon wall secretions and slow the diarrhea.
I generally recommend feeding
a bland, low residue diet until stools are normal again. This can either be in the form of a prescription low residue diet like Hills I/D that is purchased at the vet, or by feeding boiled chicken
and cooked white rice at a ratio of one part chicken to three parts rice.
in my experience tend to have sensitive GI systems and colitis is common in the breed, that is the most likely scenario. While it is not life threatening, colitis can cause lethargy and abdominal discomfort...thus, what you sister is observing is not unusual for colitis.
I would advise that you print out this consultation to show your sister so that she may compare and contrast with what she was told by her vet, use it as a discussion point if your vet conveyed something different.
Best of luck to you and best regards!