I have a simular problem with our kitchen sink, it slow to clear and the
dishwasher backs up into the sink.
I attribute it to the fact that the distance that my kitchen drain is
located far from the main drain pipe for the house and the DWV pipe. Do you
know if your plumbing is simular?
Hopefully if I can install an automatic plumbing vent, available from your
local hardware store, on my kitchen drain I can cure the problem.