swing motion in golf begins by setting a one lever--the lead arm and
club in a straight-line relations ship. It uses kinetic energy--a mass
in motion.

midway through the swing motion a two-lever system is formed by a
hinging of the wrists--the arms and club are set at a 90-degree angle
to one another. This stores potential energy--that is, energy which
may be transformed into motion.

so, swing motion consists of a mass already in motion (kinetic) and a
otential for motion created by positioning or levering a mass already
in motion (potential).

Question: How does the motion resulting from the release of potential
energy combine with the existing motion of which it is a part? How
does the motion resulting from a release of potential energy combine
with the existing motion of kinetic energy?

Example: If the golf club (mass) is traveling at 50 mph and the motion
produced by the release of potential energy is 60 mph what is the
resultant motion--or speed--of the mass?

Interesting question, but I need some more clarification...

First of all, understand that energy is energy is energy.  "Potential
energy" is not transferred to the golf ball.  The only way to have
potential energy is for your mass to be positioned at some height
above the ground (or a spring, which is not the case here).

Second, you always have a 2-lever system.  They are just coincident
with each other.

Third, you are not gaining potential energy by hinging your wrists. 
That is, unless you feel your wrists are "springy", but in golf terms,
they're generally not used as a spring.

So, when you angle your wrists, you're not moving your club up against
gravity.  Therefore, you're not adding potential energy to your club.

You are still trading potential energy for kinetic energy, plus the
energy you supply through your body.  If we take ball height to be the
ground, then the instant before the club impacts the ball, we have
zero potential energy; all kinetic.  You transfer energy, and there
goes the ball.

the club does move upward against gravity when you hinge your wrists.
The club and your wrists are already in motion (kinetic energy) and
hinging the wrists
positions the club for potential energy (to be transformed into
kinetic motion). The speed of the "all motion" energy just prior to
impact is what I am trying to determine. I'm not sure what you mean
about already having a two-lever system. Thinking of just the arms and
the club, they may be used by a golfer as either a single-lever or a
two-lever system.