This question would be much easier to answer with a packaged workbook. As is, it's impossible to tell why the filters aren't working together. If you have sensitive data, check out Anonymize your Tableau Package Data for Sharing. A few questions:
-Are all the sheets based off of the same data source?
-Do they use the same dimensions/measures?
-Does the dashboard filtering break once you add in the third sheet? Do two sheets work fine?