The first thing that I would suggest is to get a more specific diagnosis so that you can tell any future providers what exactly is going on with your son. The term "mood disorder" is a very general one that can apply to anything from Bipolar Disorder to Depression. The psychiatrist you have been working with should be able to give you a more concrete diagnosis.
To answer your question about involuntary commitment, yes, you can try to have your son committed to a psychiatric facility against his will. The basis for this kind of commitment is a determination that your son presents either a danger to himself or to someone else. The procedure for involuntary commitment would be for you to either call the police or bring him to a local emergency room (or crisis center). He will then have a mandatory evaluation by a psychologist to determine his level of dangerousness to self or others- if the psychologist finds him a danger then (s)he will commit him to a psychiatric facility for a minimum of 3 days. He will be evaluated during this time to determine if a longer stay is necessary. The providers at the hospital will help him make any medication adjustments necessary and will also help you and him set up longer-term care for after he is discharged from the hospital.
Sometimes people can be quite ill however (showing very severe mood and thought disordered symptoms) and still not meet criteria for involuntary commitment because they don't present any immediate threat to themselves or anyone else. This can be a big problem for family members who are then left with few options other than strongly encouraging their loved one to follow up with outpatient care.
I wish you the best of luck with this and would encourage you to seek the help of a psychologist for yourself if you have further questions and/or if the stress from coping with your son's struggles becomes overwhelming for you.