What is the effect of a two week vacation VS a 1 week vacation as it
relates to employee burn-out.  I'd also like to know if a 1 week
vaction provides any relief in a caring profession or if its
worthless.  Bonus for quickness

More work piles up during two weeks than one, so there's more to catch up on.

This is just one man's opinion, and just a free comment.

If you really "get away from it all", a one week vacation can have
value.  That doesn't mean that you have to take a cruise or fly to
Rome, just be so involved in doing something you enjoy, preferable
with a change of scenery, so that you forget about your work and other
matters  - not just lounge around and wonder whats happening back at
work.  IF you really want to redecorate your place, if that is goal
that can be achieved, then you have something to show for the effort,
and that could work too.
Go hiking, visit distant friends, take an intensive week's course  -
do yourself a treat and have something to show for it and to talk
about.

Good luck!