Can you attach a Tableau Packaged Workbook of your scenario?
I think Tom's request for a packaged workbook is great, because that would really help us see what's happening.
However, assuming A1 and B1 are both fields, then why not create a calculated field to use as a filter based on the parameter selection?
It would look something like:
IF [Parameter] == "A" THEN A1 ELSE B1 END
That way, you'd get A1 Values for selection A and B1 values for selection B.