Look at the image in Soft Proofing with your printing profile and rendering intent selected. Make a Hue/Saturation layer and play with desaturating Red, Magenta, and Blue, alone and in combination. Soft proofing has its ins and outs, but it's definitely a good way to avoid clipping which is probably what you're getting if we assume your screen calibration and profiles are more or less OK.
Or less scientifically, print some test strips with Red and/or Magenta desaturated about 20 to 30 points.
Edit...just to state the obvious, I assume you have "No Color Correction" selected in the driver, and "Photoshop Manages Colors" in the Photoshop printing dialogue.