How to improve sound isolation of an interior door?
A sound blanket on the laundy side would be simple.  See my answer here

Drilling and foaming the door with low expansion, door and window polyurethane foam.  The trick will be figuring out where the cardboard internal baffles go.  I would fill a horizontal row of 3 holes equally spaced, every foot.  Allow some time between fillings to let foam setup. (but not so long for the nozzle to clog (10 min?)