People who suffer from internal hemorrhoids of a given size will notice that when they apply pressure, either by straining, having a bowel movement, or even squatting, that the hemorrhoids can prolapse or push out of the anal canal. This will show up partly as you described with a pinkish color.
However, the condition you described might also be the beginnings of a rectal prolapse. This is a different condition altogether. The rectum is attached to the pelvis by ligaments and muscles. If these connective tissues weaken and the rectum detaches from the pelvis, then when you squat, it can lead to the rectum itself prolapsing out of the anus.
At this point, it is would be like a sock that pushes inside out. Any internal hemorrhoids that exist within the anal canal would also be exposed at this point.
Symptoms of a rectal prolapse include pain and blood and mucus discharge during a bowel movement as well as a loss of the urge to defecate. Rectal prolapse is a serious condition and must be treated by a physician. If you haven't been checked for this, go get checked as a precaution. This type of condition is progressive.
For more information on hemorrhoids, their causes, symptoms and treatment options, visit Hemorrhoid Treatment.