“A Rose in the Ashes” is episode nine of season one of Andromeda.
Dylan and Rommie, the embodied avatar of Andromeda, are visiting a planet hoping to get it to sign the charter for the revived Systems Commonwealth. The government refuses, and arrests them both for trying to ferment rebellion against the government. Bit of an overreaction that.
Dylan and Rommie are shipped off to a prison planet. There are a lot of prison planets, run by private companies, which makes finding the correct one difficult. Once on a prison planet, you don’t get off. Even your children don’t, as they are guilty simply because they are the children of criminals. An extreme case of original sin.
Fortunately, Trance picks the right planet out of several hundred. Supposedly just a guess. She seems to have some good guessing powers though.