My cute cochin Butterscotch has gone broody. I've
tried to break her up to no avail. I remove her from
the nest everyday and take the eggs my other hen is
laying from underneath her but as soon as I open the
hen house door in the evening she goes back to her
nest. My question is, how long will she remain this
way?

That is indeed what Cochins do best, except for being playful.
Somebody with more experience will, I suppose, give you some details about putting the hen in a suspended wire cage for three or four days, without nesting material, but with feed and water and just a small (2 by 4") piece of wood to perch on.
I broke one hen out of it by putting her on the roost after dark, it took three days. Anny