Your primary focus post-baby is restoring your deepest core and pelvic floor muscles, and part of this includes re-learning how to breathe. Because the growing baby essentially pushes organs up into your diaphragm, you may have become accustomed to short, shallow breathing–this can not only prevent you from finding nervous system relief, but also from using your core functionally. Learning to breathe three-dimensionally (into the pelvic floor, plus the side and the back ribs) will free up tension and make your core exercises more effective.
Intra-abdominal pressure also increases during pregnancy, as the growing baby causes the abdominal muscles to stretch, which ultimately means a weaker core. Intentional core exercises with breathwork integration will also support closure of abdominal separation, or diastasis recti.
Always consider the pelvic part of your core, because even if you have a c-section, the pelvic floor has been supporting the weight of your baby for 9 months, and will need some focused training to prevent/heal pelvic floor pain and dysfunction.
Another important facet of postpartum exercise is posture correction. Carrying a growing baby for 9 months can throw off your balance, cause tightness and compensation in the low back, overstretch the upper back, and even weaken the glutes. An expertly designed postpartum program should address these imbalances and work to help rebuild supportive posture—not just for pain relief, but also to set you up for the physical demand of mom duties, like feeding and carrying baby (and the endless associated baby supplies!).