What a saga, bruceha! I hope I don't ever have 2 broodies at once, knock on wood.
The first time one of our girls ( #1) went broody was last fall when they were about 7 months old. At the same time, #2 and #3 (I had 4) began laying eggs outside of their coop in our open garage shed in a tote of hay. I removed the tote and things finally went back to normal with everyone. Last week as described above, #4 went broody. She was only on the nest acting moody and screechy for one day when I removed her to the cage. But darned if #2 and #3 didn't find another nest area in the garage shed. I thought they had stopped laying due to the heat, but there, behind a pile of boards was their nest with a little pile of eggs in the hollowed out dirt. This time I left the nest there and lined it with hay and am even thinking about making an official nest box in there. Because in the coop are now the pair of month-old chicks (that failed to entice #1 when she went broody again last month,) they are in a fenced off corner, and who knows how that's going to come across to the others. Well #1 went in and had a fit when she saw them, and even left in a huff to the garage to check out the alternative nest, but it didn't feel right and she went back to the coop and laid an egg in the nest box, babies or no. She's a RIR, and the Boss, and hopefully, the others will follow suit.
ps #1 had been broody almost a week when we got the 2 chicks. We drove (it's an hour and a half ) to Estes hatchery in Springfield, on a hatch day, and so the chicks were only hours old when introduced to #1, not even a day old. Surely they still had that new baby smell. But she wanted to kill them. She was definitely broody, but I guess it wasn't for long enough or she's just mean. She took 3 days in the cage to bust after the chick intro failure. BTW we got all four hens from Estes, so far so good on their sexing-- and the 2 youngsters still look very much like pullets.