I would suggest using an attr date filter but like you stated it won't work across multiple worksheets. I'm not sure if what you are trying to do is possible in Tableau but I would be interested to find out. The easiest solution would be to create a 3 month running total in your datasource then use that measure in your worksheet.
Have you considered using 'Start Date' and 'End Date' parameters? This would allow your filter to use table calculations in sheet 1 and not sheet 2. It would be two parameters, rather than one filter, but it would conceptually solve the problem, if I understand correctly.
Thanks Eli for this workaround!
It seems like parameter date is the only solution to this issue.
I'm planning to take this approach to the business and explain them the issues with it.
Lets hope they accept!
I'm new to LOD - Can LOD's do some favor here?