Bad smell on clothes caused by plumbing?
I've never seen something like that before.  

The most accepted form of plumbing requires a P-trap to prevent sewer gases from coming back into the house.  In your case they might be flowing into your washing machine.

I haven't seen many washing machine to under sink connections before and the more typical thing is a long standpipe for a washing machine to pump the water into.  I'd be fearful that the volume coming out of the washing machine would be too much for the sink assembly to handle in a short period of time possibly resulting in the water backing up into the sink until the volume had decreased.