No, diagram one show the washer being dumped down the laundry tray vent.
You need to move the tee for the washer "below" the tee for the laundry tray.
The washer comes in "below" the laundry tray.
why does the washer drain require a lower connection, it it because the laundry is a 2" drain and the sink is a 1.5", largest drain goes lowest?