RV kitchen sink

I have both "Gray" and "Wash" on my rig (In addition to black)
Wash water is shower bathroom lavs and I suspect cloths washer if I had one.
Gray is above with the addition of Kitchen Sink or Dishwasher in case you wonder about definitions.. Yes there is a legal difference but off topic here.

When My kitchen sink fails to drain. every time for the last 15years + it's been time to go out side and "Take a dump" (Tank was full).

A cogged pipe can also do it but I've not had that happen in longer than I recall.

Do you have a P-trap or another type of trap under the sink, like a "concession trailer" trap?

Does the water eventually slowly drain out or does it stay?

Your in-line valve is one of those one-way valves under the counter to let air into the pipe, but not out, common valves in houses and RVs...

Sounds like the issues is after the "in-line" valve. Even though your snake made it through you could still have a blockage that just filled back in after the snake was removed. Try snake again and really work it and spin it in every section.

The valve others are talking about is unfamiliar to me so that could be it too, I cant help there.

Try a garden hose with trigger nozzle, spray water down the drain and this might do more than the plunger did. Risky, but it might dislodge anything. keep a hand or a towel over top so nothing sprays back in your face. use short quick burst of spray at a time.

How many grey tanks do you have? There maybe more than 1.

Is water backed up into the shower pan?
A. yes - your waste tank is full
B. no - most likely Bill.Satellite is right and you have a bad valve of some kind under the sink.

You speak of a valve and not a P-trap. If you don't have a P-trap you would have a duck bill sort of valve and using any of the devices you describe could cause the valve "bill" to fold up over itself and prevent water from flowing.

AGE Make and Model of RV will help. Doug

Is the gray tank full?