What is the ruling regarding a wife leaving for her work and visiting her relatives after her husband's death and obtaining his death certificate, knowing that she is still within the 'iddah (waiting period)? And is a person excused for their ignorance of the rulings of the 'iddah?

Your mother's 'iddah (waiting period) begins from the date of her husband's death, as confirmed by a ruling from a Sharia judge, and she must adhere to the rules of mourning (ihdad). If your mother violates any of these rules, her 'iddah is not reset; rather, it concludes when its prescribed period ends. If her committing acts forbidden during the 'iddah was due to ignorance, then there is no sin upon her.