Question:

Is it permissible for a woman to travel in such a condition where a mahram (of hers) leaves her at the airport and a mahram picks her up at the other airport?

Answer: 

Since she is travelling throughout the journey without a mahram, it is impermissible. Nabi (sallallahu alaihi wasallam) said: “It is not permissible for a woman who believes in Allah Ta’ala and the last day that she travels for three days or more (the shar’ee safr distance which is equal to 77km nowadays) except with her father, son, husband, brother or any other mahram” (Saheeh Muslim #1340).

Allah Ta’ala knows best