It's not a great match, since the publication history doesn't really fit, but many of these elements fit the short story "Breathes There a Man" (1953) by Charles E. Fitch. Originally published in Rocket Stories, July 1953 it apparently only subsequently appeared in the author collection Horses' Asteroid.

Nevertheless, the story features a liveable but very socially constrained life on Earth that many people chaffed at, and an ever-present threat of exile to the Lunar Prison Colony for people found guilty of crimes. The protagonist, and the woman he is in love with, belong to an underground of people dedicated to overthrowing the powers that rule Earth, but they are apparently betrayed, caught and "exiled" to the (vastly better/more free) conditions of the Moon.

It's not a great match, since the publication history doesn't really fit, but many of these elements fit the short story "Breathes There a Man" (1953) by Charles E. Fitch. Originally published in Rocket Stories, July 1953 it apparently only subsequently appeared in the author collection Horses' Asteroid.

Nevertheless, the story features a liveable but very socially constrained life on Earth that many people chaffed at, and an ever-present threat of exile to the Lunar Prison Colony for people found guilty of crimes. The protagonist, and the woman he is in love with, belong to an underground of people dedicated to overthrowing the powers that rule Earth, but they are apparently betrayed, caught and "exiled" to the (vastly better/more free) conditions of the Moon.