Don’t Wait for Post-Processing
To be honest, fixing mixed light scenes in post-processing is time consuming, painful, and less efficient than fixing mixed light in the field. You could process the same RAW file multiple times and combine the different color versions of the image together in Photoshop. The various versions of the image will have different white balance adjustments, however, and combining them will involve a lot of masking and attention to detail. If possible, why not just shoot it correctly in camera?
When you don’t shoot it correctly in camera, and then find it too difficult to fix in post-production, what can you do? Many photographers resort to converting the images to black and white or desaturating them. Black and white is a strong medium to help focus the image on emotion and human interaction, but often it is used as a crutch to deal with bad white balance. What do you do if the client prefers images in color? Well... shoot it correctly in camera.