Sorry to heard your story... be strong.
Do you consider to ask Dr. to visit you instead?

Do not judge others. TS is looking for best approaches to comfort her sister.
It is not easy to live with someone with mental sickness over a long period of time.

The medicine prescribe is already tackling depression

Before TS known about his sister condition, they treat her badly, but since after that, my opinion is that the family try to give what is best to the sister.
And this is also why TS is asking here to get the best opinion to comfort and treat her sister.

Sending her sister to mental health institute will make her sister happy? I doubt so, new environment, new person, more stress actually.
The best care is still those that is provided by family with love.

Anyway, it is just the way we interpret TS's word. your point is that the family is treating her sister badly and sending to mental institute is the best way out for both the family and the sister while my opinion is that the family is doing all that they can to help her sister and is looking for advice on how to get her sister to be treated by a Dr for further examination.