What to do if my grandmother was attacked by a dog and the owners won’t take responsibility?

The dog owner is liable for negligence for your grandmother's injuries.  Negligence is the failure to exercuse due care (that degree of care that a reasonable dog owner would have exercised under the same or similar circumstances to prevent foreseeable harm).  If this is NOT the first incident of the dog attacking someone, then instead of negligence, the dog owner is liable under strict liability.  Strict liability is liability imposed whether or not due care was exercised.

Another basis of liability here is premises liability.  The owner of the property is liable for your grandmother's injuries whether your grandmother was a trespasser or a guest on the property.

When your grandmother completes her medical treatment and is released by the doctor, she should obtain her medical bills, medical reports and if applicable documentation of any wage loss.  Her personal injury claim filed with the homeowner's insurance carrier of the dog owner should include these items.  Since the dog owner is not cooperating, if you can't get the insurance information, file a lawsuit for negligence against the dog owner or as mentioned above strict liability if the dog has attacked others in the past.  Prior to filing the lawsuit, if it is possible to obtain the insurance information as mentioned above, file the personal injury claim with the owner's insurance carrier.  Compensation for the medical bills is straight reimbursement.  The medical reports will document the nature and extent of your grandmother's injuries and will be used to determine compensation for pain and suffering which is an amount in addition to the medical bills.  Compensation for wage loss is straight reimbursement.  If your grandmother is dissatisfied with settlement offers from the insurance company, she should reject the settlement offers and file her lawsuit for negligence against the dog owner (as noted above the lawsuit would be for strict liability if this is not the first incident of the dog attacking someone).  If the case is settled with the insurance carrier, NO lawsuit is filed.  If the case is NOT settled with the insurance carrier, your grandmother will need to file her lawsuit against the dog owner prior to the expiration of the applicable statute of limitations or she will lose her rights forever in the matter.