Steven
there is nothing to worry about, once your household good will be place in the container and well secure including the car, it's very rare that something will happened to them. there is no problem what so ever with this method. actually almost every major company does it. nothing to be worry.
once you container will arrive to the port they will take out side the automobile and will send the container to fumigation. please note that no
international movers will guarantee the process, due the changes of regulation for some time to time. you will need to read more at government website
Dan