What is the ruling on a wife working in a hospital in a remote area 400 km away for 15 days without a mahram, then returning home for another 15 days accompanied by a mahram? And what is your advice regarding her work and seeking reward, or her staying with her husband to raise her children, knowing that she can request to join her husband after one year?

A woman's residence outside her country without a mahram (definition) is permissible if there is no fear of fitnah (temptation/strife) and no suspicion. A mahram is only required for travel. A wife working as a midwife is a legitimate and needed profession. If the country is in need of someone to perform this work, then it is preferable for her husband to grant her permission, provided that the work adheres to the regulations of Sharia (definition). Otherwise, it is better for her to remain in her home.