Link to filtered Activities tab from Contact Summary? (Drupal 7, civicrm 4.7)
One way to approach this is to build a Drupal View based on CiviCRM Activities that is Filtered to show just the activities that you want for the logged in user and display that block on the civicrm home page.

If that sounds like the way to go and you are not familiar with Views, then add a comment and I can probably do an export of a View that might get you started.