yes you can be hospitalized in a mental facility or hospital mental health unit by telling someone you are going to hurt yourself if they do not do what you want them to do, and yes you can be hospitalized in a mental facility or hospital for assaulting your parents...

here is how it works where I live...

......Anyone.... can report ......anyone ...... for being a danger to their self and others to the police. the police does what they call a ....well check.... thats when they come to you and do their own assessment of the situation.... if they find that the situation needs more investigating and that the person did make a threat of suicide or self harm or threats of action or violence against another person the police take that person who made the threats into custody (this is called arrest for probably cause threats of harm to one self or others) then they transport that person to the nearest emergency room where a mental health assessment is done. if it is found that the person is a danger to their self or others they are hospitalized in that hospitals mental health unit or medically transported to the nearest mental facility for as little as 72 hours and can be as long as needed.

if the mental health assessment shows there is no medical or mental reason for the persons violent behavior against their self, their parents or anyone else the person is arrested formally for assault, battery and other violent crimes with intent to harm someone. the person is taken to jail, booked, and shown to their jail cell and put under suicide / homicide watch while they wait for their time to go before a judge to find out how much their bail is and whether they want to plead guilty or innocent and have a trial of waive their right to a trial and the judge imposes the sentence. in situations like this the judge can impose a fine and community service and probation or jail time or remand the person over to a mental facility until the treatment providers in the mental facility can state the person is stable, complying with all treatments and is no longer a danger to their self or others.

my suggestion is not to hit your parents, even once your parents can call the police and have you removed from their home to either foster care, juvenile detention or jail depending upon your age. or if your parents feel you are having mental problems your parents can take you or have you taken to a mental facility or hospital for an evaluation and treatment.