The Family car is turned into The Griswold's station wagon from National Lampoon Vacation (1983) when they answer Rick's call from his impregnated planet.
When Morty guesses that the alien ship flew through a nebula that showed the crew their own fears, that is almost identical to the premise of Event Horizon (1997). However, the setting is also reminiscent of the similarly themed Sphere (1998), where a crashed spaceship is discovered to have picked up an alien sphere that gave the crew the power to manifest their thoughts. However, because they subconsciously materialized their worst fears, they killed each other out of paranoia.