One idea...
I know Kent RO units come with a garden hose type fitting. You could get a nice, reliable, brass "Y" garden hose valve. The washer's connection is the same thread as a garden hose anyway. The nice advantage is that these Y valves usually can turn each individual outlet on or off, so you can control the RO unit on it's own, just as you planned. I recommend the all brass ones. The ones with plastic valves break in no time with regular use, and the all plastic body valves will likely burst being under pressure 24x7...
Then, the washer's drain pipe will also provide an ideal place to run the discharge water.
If you are lucky enough to have your laundry room on an outside wall, you may want to consider running your discharge water outside. I am on a septic tank. Those units waste a LOT of water, which is basically clean enough for most things, so I ran it outside so I wouldn't be loading my septic tank down with all the extra water. As a final advantage, you can put a 55g trash barrel out there and collect the waste water for watering plants and such outside, just make sure it's closed so you don't breed mosquitos.
If your unit didn't come with such a fitting, I know that Lowe's and Home Depot have pretty extensive plumbing sections. You can easily get an adapter that is a (F) garden hose to (F) 3/4" NPT, then reduce teh 3/4" NPT down to 1/2". Then, all you need is a 1/4" compression fitting to 1/2" NPT and you're all set. You can even stick a 1/2" ball valve in there if you want.