A homework corner does not have to be a room. It has to be one spot where the work happens without a fight, and it has to be set up well enough that nobody has to ask where the pencils went. Build one for each house, and keep the core of it the same so the kid is not relearning the room every Sunday.
Local option: New Plan Care gives families in the St. Louis area in-home help so a parent can stay home: companionship, help with bathing and dressing, meals, and overnight care. Call (314) 405-0887.
Step one: pick the spot
Choose a place away from the television and the main path through the kitchen. A corner of the dining table, a desk in a bedroom, or a counter with a stool all work if they have a few things in common: a clear surface, a plug within reach, and a view that does not face a distraction. Sit in the chair you plan to use and check what you see. If the first thing in front of you is the TV remote or the dog's bed, move the spot before you buy anything.
Step two: measure before you buy
Measure the surface, the chair space, and the room the chair will pull out into. Check the door swing so a door does not hit the desk every time someone walks by. Check the cord length from the plug to where the lamp will sit. A cord that does not reach forces a cord across the floor, and that is the thing you will trip over in the dark.
Step three: set the light
Put a steady lamp on the side opposite the writing hand so the shadow does not fall on the page. Choose a bulb that does not flicker and a shade that does not glare. Plug the lamp into a strip with an on-off switch, and check that the strip stays only warm, not hot, after an hour of use. If an outlet feels loose or a plug runs warm, stop and have a licensed electrician look at it before anything else goes on that circuit.
Step four: stock the bin
Use one bin for the basics: two pencils, a pen, an eraser, a ruler, paper, and a folder for papers that need a signature. Keep a charging spot for devices at the same desk so the device does not wander off to bed with the kid. Label the bin with the kid's name, and keep a short list on the inside lid so you know what to restock. The second house gets a shorter copy of the same list, not a full second set.
Step five: mount the board if you want one
A wall board or cork strip gives the desk a place for the week's calendar and reminders. Find a stud before you drill, and use anchors rated for the weight. If you rent, check with your landlord before drilling anything. A board that falls off the wall at 9pm is worse than no board at all.
Step six: test one real session
Sit a real homework session at the desk. Time how long it takes to find the things needed, note what is missing, and see whether the kid can start without help. Move the bin, the lamp, or the chair until the first five minutes go smoothly. Then do the same check at the other house. The corner is working when the kid starts the work on their own, and you are not the one hunting for the eraser.