Combining multiple controllers on one page, without loading controllers from a controller
It sounds to me like you are looking for Modular Extensions for CodeIgniter. This allows you to break an application into modules that can be called from one another. In your case, you would have a calendar module which you could call from your other modules.
What you might be looking for is something called Layouts. Codeigniter does not have such a feature out of the box but layouts are basically delegating a (front-controller) request across multiple actions. Each action works on it's own and has it's own view assigned.
The layout will take care to put this all together into one output then.
This methodology takes care as well that you don't call one controller from another controller so you keep code apart that does not belong to each other or would get messed up because it does too much at once.
This discussion might be interesting for you: Codeigniter layouts?, the Codeigniter FAQ has more about it as well and more specifically Header and footer and menu on every page in the wiki.