It really isn't so bad to cage a broody. I don't like caging either, I free range some of mine and the rest have a HUGE yard. But a broody sits there 24/7 except to get up once a day, so caging her is really more like keeping the others out than her in.
My broody was in a cage in the coop. When I opened the coop the first morning, she stood up, so I let her out of the cage, and she did her chicken thing for maybe 20 minutes, even going outdoors to scratch for a little while. Then she went back and I shut the cage again, to keep the others out of her nest. I did mark the eggs in case someone laid in there while she was out that little while. This went on the whole 3 weeks. In the afternoon I'd hand feed her a few tomato chunks and some feed; she wouldn't get up again but she'd eat from my hand.
Worked great. As soon as there were chicks, I took the whole cage out. All get along fine.
My broody was in a cage in the coop. When I opened the coop the first morning, she stood up, so I let her out of the cage, and she did her chicken thing for maybe 20 minutes, even going outdoors to scratch for a little while. Then she went back and I shut the cage again, to keep the others out of her nest. I did mark the eggs in case someone laid in there while she was out that little while. This went on the whole 3 weeks. In the afternoon I'd hand feed her a few tomato chunks and some feed; she wouldn't get up again but she'd eat from my hand.
Worked great. As soon as there were chicks, I took the whole cage out. All get along fine.