The wire in the nest won't help. The idea of a wire cage is that cool air needs to get to the hen's underside. As long as she can keep it warm, she'll stay broody. You can just get a few sticks, some wire and some hardware cloth to make a temporary cage.
We always suspended the homemade cages from the ceiling.
You 'll probably need to treat the entire flock and coop for mites.
Change the bedding and get some 5% Sevin onto the floor, roosts, cracks, crevices, nests, etc.. Then dust all the birds twice at a one week interval.