The next and prev buttons are disabled if the active view does not have a property stepUnit.
It looks like in your case that should yield "week".
When clicked, these buttons call methods called "previous" and "next" on the active view. The view's implementation MUST include these methods.
A view MUST also implement startDate and endDate properties. These may be read-only to indicate the range that the view is looking at.
It MUST implement a read-write property called date. When that is set, the view should move to encompass that date.
So in your case, your view should move to the week that contains that date. From then, the startDate and endDate properties should yield new values.
The Calendar container will set the active view's date property when the sidebar date picker is used.
I will add some documentation for this to allow power users to do things like you are doing and add custom views.