I'll have my sister drive to the station to pick you up.
Literal
Younger-sister [target-に] car [with-で] station [up to-まで] meet [purpose-に] go [causative-させます].
~させる is the causative form — 'make/have someone do X.' 妹に marks the person being directed to act. 迎えに行く ('go to meet/pick up') uses the purpose construction. The whole sentence layers causative on top of purpose.