Check out Sheet 2 of the attached workbook. I've used the LoD FIXED function to identify the latest and the previous (second latest) dates, checked if each date is either of these two and, depending on your parameter, the right filter is chosen through another function. I've also added a title where the exact date is shown.
I hope it's what you needed.
Latest Snapshot Date v2.twbx 11.3 KB
This is one of the biggest weaknesses of our beloved Tableau
You may want to look at this idea: Use most recent date (max date) on discrete Quick Filter after extract update (if only one date is selected by default)
there are a few workarounds provided (mine at the very bottom).