Maureen Robinson takes a maintenance pod and flies it as if the Resolute was in space, yet they were in the planet's atmosphere were gravity would preclude the pod from operating. It would fall like a rock to the planet's surface.
The only way that the gas giant could be as large as it is when viewed from the Resolute would be if the planet the colonists are on was a satellite of the gas giant. In any other case it would not have a visible disk at all, let alone storms visible to the naked eye. If that was the case there would be many better and less dangerous places to obtain ammonia (other moons, rings or debris fields) .