Just so that you will understand my response, let me explain that corporation owners are NOT partners. Partners are people who own "partnerships," people who own corporations are "shareholders."
Normally, shares owned in a corporation are the property of the owners, not the corporation. Therefore, if one of two shareholders wants to leave the business, unless the shareholders have signed a buy/sell agreement or other agreements which affect their rights to sell or buy shares, transfer shares, or otherwise give up or change their position in the corporation, there is no general requirement that the other shareholder buy out the shares owned by the other shareholder. However, the other shareholder, unless there is an agreement that prevents him or her from doing so, may opt to sell or give their shares to anyone else, which may then mean that the corporation ends up with shareholders who do not know each other. Or, instead, may retain their shares and may be able to continue to derive income from the business. Or, a shareholder may file a suit to have a court terminate (dissolve) the business because the shareholders cannot agree on how to continue it. In general, there is no shareholder right to force another shareholder out of a business simply because they want to leave the business.
There is no standard value of shares when a corporation is not publicly traded. Shareholders in "private" corporations may choose to value their shares based on corporate income, corporate assets, corporate future earnings, and any other number of methods. This is one of the reasons why when attorneys help people form corporations they normally discuss the creation of buy/sell agreements and try to determine a price so that later on, problems such as the one you describe do not occur.
Because of the situation you describe and the potential for things to deteriorate, you should hire a NY attorney who works in the area of corporations law to have him or her sit down with you and fully explain all of your options and possibilities to handle this situation (such as having the company valued by a professional, dissolving the business and maybe starting a new one, negotiating a buy/sell price or payment terms, or other ways to end this matter in a way that does not harm you or the business or at least lessens potential harms you may be subject to.