[Fozzie (OP)]

If the sun expands to the orbit of the earth in its later years as predicted, will its rotation slow down to be the same as one current earth year, or are there some other forces at work which would influence this?

[imatfaal]

I think you could put the earth year as a very rough estimate - ie a freely orbiting planet with a mass much smaller than the central mass will go at that rotation; however there are many other considerations to be considered - angular momentum will be conserved (I cannot think of an external torque) and even though it is diffuse the sun will tend to act as one body rather than a set of independent shells/layers.

As a first approximation I would calculate the ang mom of the sun's mass with current radius and rotation; then put that figure back in with a changed moment of inertia (to recognize the increased radius) and work back to a new angular velocity.  This is very much an approximation as the sun does not rotate uniformly.