Is it permissible for a 26-year-old woman to go for 'Umrah with her mother and a safe company, without the presence of a mahram (brother, father, or husband), knowing that she wishes to perform 'Umrah even if it is not obligatory for her due to the absence of a mahram, and that she would be forced to stay alone if her mother travels for 'Umrah?

A woman who cannot find a mahram (definition) to travel with her is not obligated to perform Hajj or Umrah (definition). It is not permissible for her to travel for Hajj or anything else except with a mahram. The mahram for her is the means (sabeel) without which Hajj is not valid, as Allah Almighty says: "And [due] to Allah from the people is Hajj to the House – for whoever is able to find thereto a way (sabeel)." (Quran 3:97). It is by Allah's grace that whoever intends an act of obedience but is unable to perform it due to an excuse will be rewarded for it. If the mother insists on going and leaving her daughter alone, then if the daughter is in a safe place, there is no issue. However, if there is a concern for her safety, then it is permissible for her to travel with her mother out of necessity, and the sin would be upon the mother.