Problems between President & Vice President
I'll assume the corporation in question does not have a board. Generally speaking, because s-corps do not have classes of shares, the power of a shareholder is simply measured by the percentage of shares they own, unless the by-laws define what it means to be a president or vice president. If the bylaws do not define the roles then the titles of president and vice president are just honorary in nature.
If a company is managed by a board then the board could intervene. Though I rarely come across s-corps with boards.