When do we put the people who do the right thing first?
We don't. The point of human rights is that we all have them, not just "the people who do the right thing", and we get prioritised according to need. This patient needed somewhere to live prior to discharge, unlike the other patients on the ward.
It shouldn't have to be a court case- it is a medical decision. A team of medical professionals make an informed decision she needs to leave and a place is identified and she is moved- sedated if necessary.
Sedating someone and moving them against their will would be assault and kidnapping, both criminal offences, unless the patient is under section. This patient was not under section. Committing criminal offences is not "a medical decision" and, if you think that evicting a patient is expensive, the civil and criminal defence fees, fines, and compensation for assaulting and kidnapping a patient would be considerably higher and cost the medical staff their careers.
The thing about human rights is that if the unlikeable people are denied their rights, the rest of us can be too after that. It's called "setting legal precedent".