PaternitEE Conditional using Mo' Variables and IfElse

template.html

// First off, you'll want to make sure you have Mo' Variables enabled, and make sure a default value is being set for
// your field names, so things don't go crazy.

// IfElse will prevent both conditions from parsing, since this is an advanced conditional and would kill performance
{exp:ifelse parse="inward"}

  {if "{get:your_query_string_param}" == ""}
  
    {exp:channel:entries (other stuff here) }
      // perhaps a snippet of your loop template to keep things try
      
    {/exp:channel:entries}
  
  {if:else}
    {exp:paternitee:entries (other stuff here)}
      // presumably the same snippet here
    {/exp:paternitee:entries}
  {/if}
{/exp:ifelse}