Flynchick; There are a number of questions that have to be answered before anyone can answer your question.
Do you work under a collective bargaining agreement? Are you a member of a labor union? If so your contract will provide some guidance and if it doesn't or you can't find it your collective bargaining (union) staff may be able to help.
The Railway Labor Act provides a framework for Employee / Employer relations. The Railway Labor Act is a United States federal law on US labor law that governs labor relations in the railroad and airline industries. The Act, passed in 1926 and amended in 1934 and 1936, seeks to substitute bargaining, arbitration and mediation for strikes to resolve5 labor disputes.
If you and your fellow dispatchers do not work under a collective bargaining agreement, you are an at will employee. In that case the employer can make up what ever work rules they want, within the limits of general labor law. In order to bind your employer to the various sections of the Railway Labor Act, you would need to be in represented by a bargaining agent and working under a collective bargaining agreement.
If you are in a small shop, Dispatchers are considered as a Craft and Class, and you could get at least 50% + 1 people, in that craft and class to sign a showing of interest card, you could force a union election at your company. I don't think the company would like it but the RLA does prescribe that the company cannot interfere in a union campaign.