The 2″ drain that my washing machine hose goes into overflows. I’ve tried using a snake and can only get about 4′ into the drain before it snake can’t go any further. I’ve used Draino Max and it’s slightly better. I’ve stuck a garden hose down as far as it would go and it doesn’t cause an overflow. I’ve learned this was a problem for the previous resident as well.
The way it sounds to me is that you might have a stoppage down the line are you are use soap that suds to much, try a low suds soap if it does not work have a Plumber come in and run a cable through the line.