There are two solutions depending on how your school records data for divorced relationships.

If you do not use the Lives with Student checkbox to note the parent that the child lives with, add an attribute on the student record to note the parents are divorced. You can query on the attribute.
 

OR


If you consistently use the Lives with Student checkbox on the Relationships tab of the student record to indicate the parent with whom a student lives and you identify only one parent as the "Lives with" parent if both divorced parents have custody. Ensure with each query that the parenthesis are included on the criteria tab.
  1. Create a Student Query with the following criteria to find students that live with at least one parent:
    (Relationships, Relationship Equals Father

    AND Relationships, Lives with student Equals Yes)

    OR (Relationships, Relationship Equals Mother

    AND Relationships, Lives with student Equals Yes)

     
  2. Create a second query with the following criteria to find students that do not live with a parent:
    (Relationships, Relationship Equals Father

    AND Relationships, Lives with student Equals No)

    OR (Relationships, Relationship Equals Mother

    AND Relationships, Lives with student Equals No)

     
  3. Merge these queries using the operator Only select records included in both queries