Broody bantum has stopped other laying !

We have 2 bantums and two brown hybrids . Our little Buff Bantum has been broody for a couple of weeks now .The other white bantum had just started laying a few days before the buff one went broody .Now the white one has stopped laying but is more than happy in every other way .
So can one going broody stop another from laying ?

Also i have made up a wire cage for her to go in and have been putting her in there during the day but putting her back in the coop at night , as its been rather chilly at night of late . Would she be ok on her own during the night , or should i just keep doing what i am doing and wait for it to warm up , then leave her out at night ?

Many thanks Mark

Don't leave her on her own at night, they snuggle together to keep warm if it's chilly.