ANSWER:

This is not permissible as her cousin is a non mahram.

I learned that if a woman goes to a ptaxi while she’s alone with the male driver, it’s haram because the third is the shaytan. But can she go to a taxi with her non-mahram male cousin to go to the mosque to talk to a sheikh, is it halal? so there would be three people in the taxi: the woman, her non-mahram male cousin, and the taxi driver. So it would be two males and one woman in the car.