My mother has needed some serious mental health help since she left my father 14 years ago. She has gotten worse since then. I honestly think she is bipolar, she has gotten married twice since then, not that that is relevant. She has kicked out my sisters friends for less then a makeover gone wrong. She has called the cops on my sister, and now she is threatening to call child protective services on me for sticking my kid in the corner when he's in trouble instead of bribing him to be good like she dose. I would add more as to why I want her to seek help, but then I would be telling my life story. She refuses that there is anything wrong with her, and I think that a few months is a psychiatric ward would do her some good.
I know you would advise me not to. That is not what I am asking. I want to know what are the steps I need to take to get her put in a psychiatric ward? Would I have to pay for it? Or would the government?
Or if I cannot do that is there a way I could force her to get some mental help?

I'm sorry you are having so many problems with your mother and that she needs psychiatric care. Unfortunately/Fortunately it is not illegal in this country to be crazy and she is allowed to refuse to believe anything is wrong with her. She can be crazy as a loon but so long as she is not a danger to herself or others there are no steps you can take to get her `put in a psychiatric ward. She has to be dangerous and that does not mean suffering negative consequences for making crazy decisions and doing crazy things. As long as she is not threatening to physically harm herself or anyone else there is not much you can do but stay away from her.