Soapy water is not a problem with most plants (citrus is an exception). Read the label of the detergent you use and watch for heavy metals.
Remember that soapy water is used as a green form of insect control (aphids).
If possible I would move the watering spot around so you are not dumping soapy water over and over in the same spot.

You don't want to dump hot water straight into the garden so when washing whites you would switch to the sewage system or have a catch barrel that would slow down the water long enough to allow for cooling. You don't need to change out the hose if install a divertor in the drain line. Then its just a matter of turning a knob. Easy thing to install if you have pvc drain lines ... cast iron is much more of a pain and likely not worth the effort of installing a divertor. If you have cast iron you will need to move that washer drain hose after all ;o)
Mike