Should I use 2 plumbing traps at either end of a drain extension?
Double trapping is both a bad idea and a code violation in most jurisdictions - from the International Plumbing Code (my emphasis):


  1002.1 Fixture traps. Each plumbing fixture shall be separately trapped by a liquid-seal trap, except as otherwise permitted by this
  code. The vertical distance from the fixture outlet to the trap weir
  shall not exceed 24 inches (610 mm), and the horizontal distance shall
  not exceed 30 inches (610 mm) measured from the centerline of the
  fixture outlet to the centerline of the inlet of the trap. The height
  of a clothes washer standpipe above a trap shall conform to Section
  802.4. A fixture shall not be double trapped.


The length of pipe between the two traps will not be open to atmosphere on either side - normally, the vent side is open to atmosphere through the vent, and the fixture side is open to atmosphere through the drain. What will happen when you pour water into it is that it will drain fairly slowly because after moving through the first trap it is compressing the trapped air between the traps.  

On the other end, in order to go through the second trap, it would need to pull air through the other trap to avoid having to create vacuum.  This prevents the pipe between the two fixtures from completely draining.