Have you tried a wire bottom cage? I believe the wire bottom cages work because they can't keep their bellies warm and that is what breaks the broodiness. At least that is what I've read. You are supposed to leave them in the cage full time. I think letting her out at night is counterproductive to what you are trying to do.
If you do want more chickens but don't want boys, let her sit on fake eggs for about 21 days and then get sexed day old chicks. That's what I had to do for my broody because none of her eggs hatched. You take a chance she might reject them though.
If you do want more chickens but don't want boys, let her sit on fake eggs for about 21 days and then get sexed day old chicks. That's what I had to do for my broody because none of her eggs hatched. You take a chance she might reject them though.