I have never moved a broody hen myself. My coop is set up so I can lock them in the nest they go broody in and open up a feeding, watering, and toilet area. I'll pass on what someone else does.
How to move a broody hen
https://www.backyardchickens.com/forum/viewtopic.php?id=162759
You will note that when they move them, they do not lock the hen in with the nest. After a couple of days, they just remove the outer box so the hen can come and go as she pleases. This still allows other hens to lay in her nest. I'm sure with many people this would be OK, but the main reason I would consider moving a broody is to lock her where the others cannot lay with her. The main reason I am concerned with others laying in her nest is that she might come back from her daily constitutional, find another hen on her nest, get confused, and go to another nest. I'll mark the eggs anyway and I don't mind checking under her once a day to see if others have laid new eggs in her nest, but I am not always around to be sure she goes back to the right nest.
I'd be concerned that she might poo in of her nest if I kept her locked in the box for two days, especially if she already has eggs. Maybe if it is dark enough and she thinks it is just one long night, she can hold it? The point about suffocating her is important. With this method you are keeping her without water for a long time. You sure don't want to keep her in a hot stuff box for that length of time. Dehydration is also a concern.
I'd suspect that making the nest she is going to as dark as possible, especially for the first few days, would help her accept the move. I don't think I'd leave her locked inside the two boxes quite like this person does but give her an option to get off, eat, drink, and go poo, realizing it probably does reduce the chance of her staying broody some. My main concerns are the heat and dehydration more than suffocation. But remember I have never moved a broody.
I'll include another thread that talks about why to move a broody. You may already know all this and may have made up your mind, but you might pick something up from this thread. At least you'll get a few different opinions or maybe someone else reading this thread can benefit.
Isolate a Broody? Thread
https://www.backyardchickens.com/forum/viewtopic.php?id=213218
Good luck with the broody.
It is an exciting time.