Is it permissible for a mother observing the 'iddah (waiting period) after her husband's death to travel to perform 'Umrah before her 'iddah ends, and what is the expiation for that if it involves sin?

It is not permissible for a woman observing the 'iddah (waiting period) after her husband's death to go out for Hajj or Umrah. However, if she contravenes this and performs Hajj or Umrah, her Hajj is valid, and she must seek forgiveness for what she has done. Likewise, those who encouraged her to do so must also seek forgiveness.