The basic guidance Stephen King provides a writer to be with is to write about something they really know about. This way you can mix real things with your own plot and make your story credible. Which is basic to catch reader's attention.
Read the story now
Unfortunately, from the very first page, it looks like you have no idea how a mental institution works. Or about the schizophrenic disease symptoms, which may sound nearly offensive for people living with schizophrenia or psychosis.
There is no chance in any place in the world, nowadays, at least, you can "check" someone into a mental hospital the same way you go to the till when you shop. In reality, the mother would be advised to look for treatment, in the first instance. Asylums even do not officially exist anymore.
Such a story would be maybe possible if set during the 60s not today (Girl interrupted, Sucker punch, and similar).
Based on such a fragile foundation your plot, even though catching, looks like a good navy crew on a sinking ship. There is nothing they can do but leave it quickly.
My personal advice is before you write a story get information about what you want to write about. Make the reader wonder "could this be true?". That is the feeling filling pages with glue and make a story difficult to put aside even after finishing it.