Get the rubber feet to put under the laundry machines they sell on Amazon. Those helped on our stackers. Also, if you have the space, I wouldn't open the wall cavities, either just add sound dampening insulation to the utility room side if you have the space, cover in plastic and call it a day, or, add a second layer of 5/8" sheetrock. You can open the walls and insulate with Rockwool too, but the studs will still translate a fair amount of vibration noise through the wall. You want continuous barrier and density, hence a second layer of sheetrock. Lastly, if you have any wall hanging rugs or tapestries, you can hang those where the utility room wall meets the living room wall. We collect Navajo rugs and use them secondarily as sound dampeners in noisier rooms.