My sister was DPOA for our aunt until September of 2016 and I am now the DPOA. Is it possible to review old bank statements without legal recourse?

As POA for your aunt, you should have the right to request all bank statements from the bank directly and review them. There's no legal reason that you can't. As POA, your responsibility is to be sure your aunt's money is being used properly for her care and well-being.