How can I betray Maven Black-Briar?

As per the comments, Maven Black-Briar is an "essential" character, meaning there is no way (outside of console commands) to kill her off.

She plays a part in several other quest-lines, namely the Thieves-Guild and the Dark Brotherhood, aligning herself with the "darker" side of Skyrim.

The only quest that causes any harm to her persona is to go see a man about a horse.

Additionally, the Black-Briar Lodge also contains some hefty loot, and an Unusual Gem, so I'm sure you can have some fun beating up her henchmen and stealing her stuff. But even then, when you talk to her after this, there is no difference in her interactions so she either

• doesn't give two hoots, 'cause she's rich and powerful and has her head stuck up her own butt

  or (more likely)

• The dev's didn't actually allow any differences to be made to her AI, so anything that you can do is entirely for the player's benefit only, with no outside effect on the rest of the game.