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I think I understand your problem, but it'd be much easier if you could share a packaged workbook. If you have sensitive data, perhaps you could try to recreate your issue using some of the dummy data sets that Tableau provides out of the box. (click the little house icon tab near the top right and start from one of the Saved data sources).
It sounds like what you're really after is a parameter + calculated field combination. I employ this combination all the time. Assuming you have a field that provides the Tenant name and another that provides the Parent name, the setup is as follows:
1) Create a string Parameter titled "Parent or Tenant" with List options of "Show by Tenant" and "Show by Parent"
2) Create a calculated dimension field named "View By":
IF [Parent or Tenant] = "Show by Tenant"
THEN [Tenant Name Field]
ELSE [Parent Name Field]
3) Put your new "View By" field on your view in lieu of the Parent or Tenant and then expose your parameter to allow the user to toggle which dimension occupies the space.
I already had the parameter + calculated field combination set up almost exactly as you described, but it still didnt solve the issue.
I was able to solve the problem by making the original worksheet into two worksheets, then just combining them on the dashboard. It doesn't look as pretty, but its functional and accurate. I think the problem was cause by the many different filters and levels of detail I had on the original worksheet. Some of the levels of detail weren't required for all calculations on the original worksheet, so it was calculating some things at a different levels.
Thanks for your help!