Re: Sinknolumbing question
For the final word, I'd post your pic on Terry Love's forum, but I would think that the sink trap should be for the sink only, and that washer should also have a trap of it's own, and hit lower down. Plus I see no evidence of a vent for either.
My guess is the rush of water from the washer is hitting hard enough that it creates suction--then ***** the water from the trap on the sink--hence the stink...
You could fix the vent for the sink by adding a dry vent/ "mechanical air admittance device" like is used with island sinks as someone has mentioned... which would be easier than trying to vent to outside from what I can see. The washer though still might create more suction that one of those could handle, and not eliminate the odor.
Washers generally discharge into a standpipe with a wet trap at the bottom--and from there the discharge goes into the stack/main waste. You have large amounts of water discharging, and the stand pipe allows the rush of water to drain quickly--and also "vent" by drawing in air vertically as the rush hits--so maybe both sink and washer would need venting in your case.
You might get away with sizing down the p-trap on the sink, and squeezing in a separate trap for it--with a mechanical vent in place--but I think the washer discharge would still want to suction that water out of it when the washer discharges
It would be worth it to run it past the guys on Terry's forum for the best fix...