What version are you using? That functionality does exist in 3.6 and later. The "preview" is of the content in the admin view, but if you click on the linked object name in the "approval" area of the collaboration view, it will take you to a full, real preview.
You might be able to modify that template to use the real preview by combining it with elements of the real preview template.
The link to the object in the collaboration inbox (after approuval but i don't think it matters here) is:
<a class="status_read" href="/index.php/mobilite_admin/collaboration/item/full/4"><i>Journal d'entreprise</i> a été approuvé pour publication</a>
where 'mobilite_admin' is the site access name of the admin site.
When clicking this i am sent to a poor "Default object view. Click to create a custom" view. On the other hand in the content module I can use the preview function that shows me my content in the actual end user site.
This is what I can see. Is there anything misconfigured ?