I would definitely move her, nest and all. The chicks could easily fall out of the nest before mama is ready to leave the nest and die.
I had a chicken go broody and hide her eggs this year too. I found her eggs in a planter on my back patio. At the time I didn't know she was broody, just thought she was laying her eggs in the planter, and since I had an incubator already going I took them and stuck them in the incubator.
Later, I noticed she was acting strangely, running around like she was looking for something and trying to get into the aviary where the little button quail are. I guess she thought they were babies.
So I ended up putting her eggs back and putting her on them and she settled right down. The problem was, I lock my chickens up at night so the critters can't get them and with her sitting on the eggs outside the coop, I was worried, so I moved her, planter and all into one of the aviaries that was empty. She didn't mind the move at all, as long as she knew her eggs went with her. So I don't think you have to worry about her abandoning the nest if you move her. She seems pretty determined.