I am sure that you did the right thing. I would probably have done the same, although I hope not to have to be in the same situation.
For a healthcare worker to be drunk on duty, is unacceptable. Similarly, I believe it is also unacceptable for your superiors to fail to act, and maintain their duty of care to the patients at the hospital.
Perhaps, the only thing I would have done differently would have been to tell the appropriate professional body (College of nursing), about their member's unprofessional conduct. These organisations have a lot of power, and will not back down or push it under the carpet if they are told of misconduct. They have the power to cancel professional registration, or to temporarily suspend it pending professional treatment.
To give an example of how seriously misconduct may be treated by such a body: a nurse was pulled over for speeding, and told the officer that she was a nurse as part of a speech to try and avoid a speeding conviction. The police officer contacted the college of nursing. They investigated, and found her guilty of bringing the profession into disrepute - her membership was revoked, and she was not able to work as a nurse thereafter.