Is there any way to display relative velocities either as vector arrows or on a color map?
You can create a new Vector Field using New->Result. The formula to create the relative velocity field is:
U - (omega x (XYZ - origin))
where U and XYZ are existing Vector Fields, omega is a new vector variable for your angular velocity, origin is a new vector variable for the origin of your coordinate system, and 'x' is the cross product operator.
For an example of creating new results see the tutorial "Fluid Flow Around a Sphere: Theory Comparison".