I suggest you use parameters, a start date and end date parameter, instead of a filter. When you filter you're actually removing the data you don't filter for from the underlying data set hence you can only do a YoY using parameters as filters.
Once your user enters a start and end data you are able to create a calculated field which will define whether the date period should be displayed or hidden. This thread has some guidance in that area: Non quarter end month calculation
Also this link can help with the parameters/calculated field: Tableau Advanced Date Filters
In your case the calculated field will be something along the lines of:
IF Date >= StartMonthParameter AND Date < EndMonthParameter then 'Show'
ELSEIF Date >= DATEADD('year',-1,StartMonthParameter ) AND Date < DATEADD('year',-1,EndMonthParameter) then 'Show'
Will be of help if the file can be updated
I don't have your version of Tableau so can't do the work for you as I can't open the workbook.