How can I make an "Accordion Widget" in WPF?

You're not seeing the Expander because you redefined its template. This one should work better :

        ...
        <Expander.Template>
          <ControlTemplate
              TargetType="Expander">
              <Border
                  BorderThickness="1">
                  <Expander Content="{TemplateBinding Content}" Header="{TemplateBinding Header}"/>
              </Border>
          </ControlTemplate>
        </Expander.Template>
        ...