There is no need to remove your existing Twitter account from its current broadcaster, which could result in lost data associated with that account. Instead, create an additional broadcaster and connect your new Twitter account to it.
To change the Twitter account shown in your website’s sidebar, change your site’s primary broadcaster. This can be selected by navigating within your control panel to Website > Site settings > Basic.
Complete and current information on how to use NationBuilder is available in the documentation section.