I don't think I could even let her sit for 3 weeks......If she does not eat/drink/poop well or if she does not quit after a week or so of 'gentle nudging' to break her broodiness I will do the broody cage. I just hate to do it if I can avoid it. Broke my broody GLW without the cage after a few days. Can't have more chickens otherwise I would let her have a few fertile eggs.
