Is it permissible for a woman to travel by land with her relative (her maternal aunt's husband's brother-in-law), who is 50 years old, accompanied by his wife and children, or by air alone with her children, without a mahram, relying on her family to meet her upon arrival?

A woman is not permitted to travel except with a mahram, except in cases of obligatory travel, such as the obligatory Hajj or Umrah, or emigration from a land of disbelief when unable to practice the religion and fearing fitnah. In these cases, it is permissible to travel with safe company, and in the case of emigration, even without company. Your current travel is not obligatory.