You could make exactly the same argument that she wouldn't be rude to come along uninvited if the group met at a restaurant -- on the ground that someone not part of the marriage "has no right to usurp" her sacred marital right to be at her husband's side.
The club isn't telling her to leave the house. Her husband is. The club hasn't told her anything. If anyone is "usurping her rights," he is. (As to the club's rules "interfering with her right to be on her own property" -- well, how is that different from the Bunco situation? Isn't the kitchen or the living room "her own property" too?)
He's telling her that because he belongs to a club that requires him to provide an empty house when it's his turn to host. But he is the one telling her, not them. Maybe he is rude to do that; it just depends on their feelings about it.
She is rude to both her husband and the club if she insists on staying. She may be completely justified in being angry at being placed in a situation where she either has to clear out or be rude. Suppose instead he had invited dinner guests without asking her first; she'd certainly be justified in being annoyed at that, but she'd still be rude if she refused to speak to them during dinner or flip on loud music or start doing yoga in the middle of the living room while they are conversing there on the grounds that she has the right to do what she likes in her own home. Justifiable annoyance at your spouse isn't a license to be rude to others.
What this comes down to is whether it is okay for a spouse to ask the other spouse to clear out of all or part of the house during a members-only meeting of a private group that requires it of its members when it's their turn to host. For some families, it is okay; for others, it's not. For the latter, if their family will not cooperate, then that's not the club for them.
But that doesn't make it wrong for such groups or such rules to exist. The LW is trying to win her disagreement with her husband by turning it into an objective, one-size-fits-all etiquette matter, and it just isn't.