When the dishwasher or the washing machine dispenses waste, it starts filling the kitchen sink instead of going through the plumbing pipe to the outside

You have blockage in the horizontal drain line in the wall that won't allow the addition volume the DW discharges. The solution would the "J" bend from the trap and send a snake up into the wall, (see image) you will hit a bend about 8 inches in but once around that you only have to put out 5 feet more. After, pour hot water into the drain.