Views with filter on "main" and "additional" taxonomy terms
You should use the Representative Node pattern. That is that your View on the taxonomy refers to another View that collects a Node based on a particular filter (a checkbox in your example but just as easily a flag like &quot;Sticky&quot; or &quot;Promoted&quot;).
There are two representative node patterns in Drupal 7. The first, which is builtin to Views, is a little less flexible (you can only sort on one parameter and you can only get one result). The second is the contrib module Views Field View which has fewer limitations but is a little harder to set up (you have to pass the contextual filter yourself).
Views 3

Firstly create a View on Content (filtering on Articles) with a contextual filter on the field containing terms from your Taxonomy. Check that it works by passing in a term ID that you know has content. You should get a number of results.
Next create a View on your Taxonomy and have it list out the terms.
Add a Relationship (Advanced &gt; Relationship) using Taxonomy term: Representative node
Sort on your specifier (your checkbox field or sticky/promoted)
Select your first View on Articles and apply.
Add a field Title and use the Representative node relationship. Continue adding fields using the relationship.

Views Field View

Firstly create a View on Content (filtering on Articles) with a contextual filter on the field containing terms from your Taxonomy. Check that it works by passing in a term ID that you know has content. You should get a number of results.
Then limit the number of results. Possibly 1 in your case. Turn off paging.
Lastly filter on how you want to select your Representative node. The checkbox, or stick/promoted.
Next create a View on your Taxonomy and have it list out the terms.
Add a hidden tid (term ID) field
Optionally add Title and other fields.
Then add a field of type Global:View
Select your View previously created. Pass in the term ID.