Are the sins of a woman who gives birth absolved due to the pain she endures during childbirth, and consequently, is the obligation of prayer waived for her?

When a woman gives birth, she experiences pain and suffering, and this pain atones for her sins. If she is patient and seeks her reward from Allah, that will increase her recompense and good deeds. Generally, calamities are expiations for sins, and if accompanied by patience and seeking reward, the person afflicted will be rewarded for them.