Clone the ContactInformationTemplate and create a ContactInformationParameters version that does not use the current tiddler in any way (and thus does not need to be transcluded as a template).

If you've been messing with your ContactInformationTemplate, feel free to start with this version:

<h2>Information about {{!!title}}</h2>

<ul>
<li>''Email'': {{!!email}}</li>
<li>''Phone'': {{!!phone}}</li>
<li>
  ''Family'':
  <$transclude $variable="list-links-draggable" tiddler=<<currentTiddler>> field="family" />
</li>
<li>''Manager'': {{!!manager}}</li>
</ul>