Your breathing technique has a bearing on the smoothness of your bowel movement.
Generally, "abdominal breathers" are more relaxed than "chest breathers". Abdominal breathers breathe into the abdomen whereas chest breathers breathe into the chest.
To determine which kind of breather you are, put one hand on the chest and the other on the abdomen. I would suggest you compare what is it like to breathe into the chest and, to breathe all the way down to the abdomen. When air reaches the chest, the chest expands outwards while the abdomen contracts inwards. Try shallow breathing a few times to observe this pattern.
Most people, including me, are chest-breathers. It takes conscientious effort to train oneself to breathe into the abdomen.
Before abdominal breathing, exhale through your mouth slowly. Try to breathe out as much air as possible. Put one hand on the abdomen to feel the inward contraction.
Inhale with nose slowly. Put hand on the abdomen to feel it expanding outwards. That is one cycle of abdominal breathing.
Cultivating the habit of abdominal breathing activates abdominal muscles which in turn encourages peristalsis. Longer, deeper breathing also "unwinds and de-stresses".
Life is not a bed of roses. At least you and I can afford to breathe in more air.