You could do a look like this if you choose the right linoleum. Be careful or it could look cheap. The black & white pic is probably tile but could be done in linoleum. Second is marmoleum. Get the real linoleum (not shiny)

I deal with a lot of laundry too, especially at times when the kids will bring me a weeks worth of clothing. Where I am we pay electricity at different rates depending on the time of day so if I don't keep it somewhat organized it will start to overflow because weekdays I can only do loads in the evening to save $. One thing I did was to install cabinets with doors above the washer and dryers. I just re-used ones from our kitchen tear out, but you can usually get second hand ones fairly cheap if you are on a budget. This keeps all our laundry washing/dryer needs tucked away. We also have extra batteries and lights stored in there and our first aid and medication in the other cupboard for us and our livestock. We also have a laundry sorter for darks/whites/linens. It looks like you already have a great set up for that with your bins. Not sure how old your kids were, but they can start at a pretty young age at putting clothing in drawers if label the drawers with pictures. I think my kids were about 5 when they started doing it. It wasn't perfect of course, but they would have to put them in the drawers after I folded the clothes. It helps if you don't have clothes that need hanging. My one teenage son still gets all his clothes in drawers because they never seemed to make it on hangers in the closet. I would designate a folding area for the counter above the appliances and the counter above the cabinet as where folded clothes stay until their owner puts them away. I'd also maybe put some hooks or a rod above your laundry sorter. This would allow you to have clothes that are hung put on the hangers until they are put away.

I think you might have to have a carpenter build a cabinet around the washing machine for the dryer to be placed on. I don't think a shelf would be strong enough. There might be some photos on the Internet of such a shelf...

I am torn with this design, with the light being best for the kitchen/living room spaces, and hence placing the utility room in the middle which is the darkest place in the house is the deisgn plan. Does this work from a function of house the house works, as kitchen and dining area are removed from the rest of the house with access through the porch or through the music room. Any thoughts woul d be great, Regards...