Report to prompt for one date but be used for multiple date fields

Not tested, and this may warp your brain a bit, but I think we can get this working with this approach.

Create a new formula date field called  [Enter Beginning Date] where the formula is 

Min([Date Received],[Date Submitted])

Create a new formula field called  [Enter Ending Date] where the formula is 

Max([Date Received],[Date Submitted])

This make an <ask the user> report asking for those two field values.

While, this may be confusing to us, the intention is to make it stupid simple for the user.