The move was simple so a characters and puppeted IK rig were single use. The dad's arms and the baby's position and rotation were controlled by one null at the wrist. The baby's arms, legs and head were keyed to give the baby some overlap.
The pee stream was built with Trapcode Particular. The emitter was linked to the diaper so the baby's rotation would be reflected in the stream. Layer One was the stream and splash of Auxiliary particles against an invisible 3D layer. Layer Two was an invisible stream and Auxiliary particles sticking to the invisible 3D layer to create the shirt's moisture. Both passes were blurred and had their alpha channel's crushed to make it more splattered and less circular.
The original plan was to have the diaper fall off but in the midst of my sleep deprivation I totally forgot to do it. I realized the oversight after I uploaded.