My suggestion would be.... move mama and chick to the floor box...if you reach under her (carefully) and get ahold of the chick you can move it to the floor box... mama will follow! Trust me! LOL
... but before the move... set the box in a position that allows you to place a barrier of hardware cloth around the box, including a few square feet of floor space, a corner away from the pop door would work well. With broody and chick in the box you can place food and water within the fencing area for the first few days. This will allow mama and chick to bond and for the young one to learn to respond to her vocal cues. It will also allow the other 2 hens to become familiar with the sight (and sound) of the chick.
After about 2 days, maybe 3... you can take down the wire barrier and allow mama and chick to roam within the coop and run as mama sees fit. The thing you will need to watch for is excessive aggression from another hen (make sure there are multiple food and water sources to help reduce resources being a source of conflict) and you will also need to provide a safe box on the ground in the run if there is a ramp which needs navigated. Chicks are often good going down, but not so much with getting back up the first week. A box in the run will give mama hen somewhere sheltered and dry to rest with the chick if it gets cold, windy or rains when they are outside. Make sure you check each day that the little one made it back up the ramp and assist as needed.
After this first broody experience you will have a much better idea of how your flock responds to little ones and hopefully any future broodies can just have a floor nest after hatch with no barriers needed. Some flocks are very broody friendly, but sometimes folks have a flock member or two which just causes a need for more security...
Thanks for all the great advice. I certainly have some work to do out in the coop!