What is the direction of a comet's dust tail before and after perihelion?

Comet tail always aims away from the sun, as it's torn from the comet's gas cloud by solar wind. It trails slightly behind, as the comet moves along its orbit while the gas travels directly away, but that's relatively minor - the speed at which the gas and particles are pulled away forming the tail is much higher than the comet's orbital velocity.

Your visualisation shows it trailing behind the comet as if it was moving in some gaseous/liquid medium that stops the lighter particles while letting the heavy comet head travel ahead. This is not the case - as the comet is far away from the sun, the gas cloud just forms its atmosphere and travels with the comet. As it approaches though, the intensity of solar wind increases and it pulls away the atmosphere which can't be protected against it by magnetic field or strong gravity, as the comet has neither.