The method I would suggest is using a parameter to filter the dates in the view. Using a parameter will allow one parameter to filter the views. The below links contain information on using parameters to filter views.
Hope this helps!
Why dont you keep it simple have them as tabs side to side and they shall have there own date filters..
I had the same requirement but it was creating optimization issues for me to have these two sheets in one dashboard with one date parameter..
i explained to my client and he found the later one much simpler for himself..