I am having two problems that I think are related. Backstory, just moved into a 2010 built home. Replaced the contractor grade dishwasher with a new one. Kitchen has two sinks. When the disposal is used, the water shoots up in the opposite sink. Additionally, the dishwasher is leaving food, sediment on the dishes. Took the trap apart and no clog was present. Hoping to find a solution before calling a plumber.
You should be using a baffle tee to connect the disposer drain to the other sink outlet, prior to the trap.
This will require significant alteration of the existing setup, but will fix your problem.