There is a thread here that's about 2 years old regarding exactly what you're experiencing. It seems a P trap won't work on a moving RV, so the manufacturers came up with a "one way valve contraption" (I'm trying to be nice) to drain the outside sink into the black tank. You're not the first one to have that valve fail and black tank effluent perk up into the sink. If you're still under warranty, take it to the dealer and have them fix it right, if you're out of warranty and need to do it yourself, you can "try" the replacement valve route, but what some have done is remove the drain from the black tank, seal the tank so it won't leak or smell and then build a new drain for the sink that goes into a blue tank or into a 5 gallon bucket.
Do a search for outdoor sink drain, or outdoor sink and you should get a lot of good information.
I can imagine how you felt with "brown dishwater" YECHT