You can use this calculated field to determine if a code has records with both values:
TOTAL(MIN([Mechanic Internal/External]))<>TOTAL(MAX([Mechanic Internal/External]))
which is a table calculation which you then put on the Filter shelf, select to keep only True, and choose Compute Using -> Mechanic Internal/External.
Essentially, it partitions data into buckets for each ATA Parent Code and then checks if each bucket has both values present. If yes, it returns True, otherwise - False.
I was playing around with Tableau 8's sets for this, but I like Dimitri's clever solution.
I also noticed that your Mechanic Internal / External field may not be working correctly. There is a space before OUTSIDE in the Mechanic field --- " OUTSIDE VENDOR MECHANIC" --- and you didn't have this space in the Internal / External IF/THEN statement. You could add the space or, perhaps better, use TRIM([Mechanic]).
Thanks a bunch! That worked like a charm.