Your parent has started eating at the table again, which is good news, and it also means the table now has a job it was never sized for. Before you move a chair or buy anything, stand where the walker will stand and check what the room gives you.
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Measure the pull-out first
Pull the chair back from the table the way your parent will. Measure from the table edge to the nearest wall, cabinet, or doorframe behind it. You need room for the chair to slide out, for the walker to sit beside it, and for your parent to turn around without hitting the counter. Write the number down. If the gap is less than the walker's width plus the width of a seated person, the table is in the wrong place, not your parent.
Check the chair swing
Most people do not notice the arc a chair makes until someone is sitting in it. Sit in the chair you plan to use, then rise and turn toward the walker. Note which way the arms or back catch on the wall, a radiator, or the chair next to it. Pick the chair that clears on the side your parent turns toward. If the arms catch, check whether an armless chair with a firm seat works better.
Ask about the seat height
Stand up from the chair without using the tabletop. If your parent has to push off the table, the table is too low for the chair or the chair is too low for the way the body rises. Compare the top of the seat to the bend of the knee, and the table edge to the lap. Your parent should be able to rest a forearm on the table without hunching.
Walk the route
Walk from the kitchen to the table with a full plate, then from the table to the bathroom or the sofa. Count the doorways, the rug edges, and any step. Anything you have to think about on the walk is a route problem, and it will be a worse problem on a bad day.
Decide before you move anything
Write down the chair you will keep, the side the walker parks on, and the one place a plate or cup can sit without a reach across the table. Then move the table or the chair once, run the full sequence with your parent, and change only what failed. If nothing you own can clear the walker, a smaller table or a different seat is a legitimate answer. Your house is allowed to be the limit.