Who can sue when a parent is given the wrong medications?

There has to be an injury caused by the wrong medication.  If there isn't any injury, there is no case.  It would be advisable to wait and see what the doctor's medical report states to determine whether or not there is a case.
If your mother was injured due to the wrong medication, prior to filing a lawsuit, it may be possible to settle the case with the rehab center's insurance carrier.
Notify the insurance carrier in writing of your mother's claim.
When she completes her medical treatment and is released by the doctor or is declared by the doctor to be permanent and stationary which means having reached a point in her medical treatment for the wrong medication where no further improvement is anticipated, obtain her medical bills and medical reports.  Your mother's claim filed with the rehab's insurance carrier should include those items.
Compensation for the medical bills is straight reimbursement.  The medical reports will  document the nature and extent of her injury/ailment from the wrong medication and will be used to determine compensation for pain and suffering which is an amount in addition to the medical bills.
If the case is settled with the rehab's insurance carrier, NO lawsuit is filed.
If you are dissatisfied with settlement offers from the rehab's insurance carrier, reject the settlement offers and file a lawsuit for negligence against the rehab.
Your mother should be listed as the plaintiff in the case.   If there is someone who has been appointed to make decisions for her such as a conservator, guardian, someone with a durable power of attorney for healthcare, that individual can file the lawsuit on behalf of your mother. 
If the case is NOT settled, the lawsuit for negligence against the rehab must be filed prior to the expiration of the applicable statute of limitations or your mother will lose her rights forever in the matter.