This is possible with two dashboard actions, you have to use the field by which you want to filter on rows or columns of the worksheet you want to show. For instance here is my dual axis map:
I want to show Tract Name values in one worksheet when selecting a polygon and County Nam in another worksheet when selecting the highway lines. These fields are in the Detail shelf in my map. I put both worksheets with detail onto a single container in a dashboard.
Finally set up two action filters with the specific target field:
That should do the trick, other details may include hiding the worksheet titles to tidy the dashboard.
Hope this helps!