What leads you to believe the Relentless has a brig?
Um, Captain Darling mentions it on page 320? "Maybe I should burn your laser off its swivel mounts, board your little turd and introduce you to the sailors in the brig."
So what? I don't believe everything (anything) government types say. Do you? I bet you can't wait for the free, high-quality medical care for everyone that Barry has promised.

It's
First Officer Darling, by the way.
Discretion being the better part of valor, Cap'n Doris wisely decided not to call what may or may not have been a bluff. After all, what sort of treatment could the Hero of the War of the Worlds expect if any UW ships did show up?
Are we reading the same Webcomic? The UW has already backed down under threat from Ceres once, what makes you think they would destroy a Belter ship with impunity, especially Doris and Fiorella's ship?
Well, for one thing, I write these stories.

More importantly, the UW navy has proven itself to be impulsive and Doris caught them with their pants down. I would not count on that happening again. Sure, shooting Cap'n Doris
could cause trouble later on, But nailing after she humiliated the
Gamma Conqueror, would mean a major career boost for 1st Darling.
Right. So you've never operated anything that required more fuel than an automobile, then. We're talking about great distances here.
Does an 18-wheeler count? Did that once with a full load in the mountains while the owner slept. Man, that was a rush. Other than that, you got me, pardner, I don't own a spaceship... yet. However, EFT is in the
future. "Desktop" nuclear fusion is cheap, reaction mass is abundant and it's the Delta-V that counts, not the distance, per se. Finally, as Johnny Carson used to say, "Buy the premise, buy the bit." Thanks for playing.