Considerably more facts are need to answer this question. First, what conditions require psychiatric hospitalization and how do those conditions differ from the conditions that required the hospitalization. Second, do her admitting/treating physicians agree she should be in a psychiatric hospital. Has she been evaluated by a psychiatrist in the hospital where she is admitted. If her physicians believe she needs psychiatric hospitalization more than the current treatment she is receiving, those physicians could recommend a transfer to a psychiatric hospital, the psychiatric hospital will have to accept the transfer, and you will have to sign a consent,
An "involuntary commitment" usually requires a hearing in a court for the committment, and there usually must be some showing the person is a danger to herself or the public due to her psychiatric condition.
If this something a hospital administrator has suggested, instead of a physician, I would be skeptical and ask a lot of questions.
You will probably need an attorney for an "involuntary committment", and it will have a significant detrimental impact on your relationship with your mother. If you have siblings, I would also recommend you speak to them and get a consensus, if possible.
This answer does not constitute legal advice or create an attorney-client relationship.