I have tried vinegar and baking soda and a commercial cleaner. When I use the plunger the water in time will go down. What should I do first? Should I take my dishwasher apart or the attempt to clean the trap? Thank you for your help!
It sounds like your dishwasher drain line is not installed correctly. You should have a loop so the drain line goes above the bottom of the sink before it goes to the dishwasher. Generally, the loop is attached to the bottom of the countertop itself.
Without the loop, when water is draining from the sink, it will naturally flow down the dish washer line. If there is a restriction in the sink drain, it will make things even worse, as the dishwasher drain is likely to the path of least resistance.
The loop prevents water from draining down the line so long as the standing water level is lower than the high point of the loop. If your sink is almost completely full of water without the drain stopper in (to the point it drains into the dishwasher), you have an upstream clog that must be dealt with either way (you'll have the same issue with the dishwasher draining into the sink and/or not draining at all).
I don't see any reason it would be the dishwasher. The drain or, if you have a a disposal, is plugged up. The bottom of the dishwasher is the low point and so it backs up mostly there instead of into the sink. The drain needs to be cleaned for a proper flow. With a disposal the dishwasher outlet may go into the disposal and it could be the disposal that is plugged. In any case, it's best to also have an air-gap installed. Essentially the hose from the dishwasher goes up to a device that protrudes above the counter or sink such as through a hole for a rinse wand. Then another hose goes to the plumbing or garbage disposal. That air gap above sink level prevents water backing up into the dishwasher and prevents a vacuum sucking water back into the dishwasher. It's required in some states. However, it still may be slow to drain from the sink until the line is properly cleaned out. It could be the disposal, trap, or something further down the line like cooking grease.