Your first sentence says "dripping ceiling vent" and the rest addresses "condensation inside the skylight"...
If your roof vents are dripping, that is a normal occurrence. They are usually single thickness plastic domes with metal framework. The outside cold makes them cooler than the interior air and humidity inside the trailer will collect and condense on those cooler surfaces and cause dripping. You can reduce it by opening each roof vent slightly to create a draft. That will reduce condensation and dripping.
Now, as for the skylight, usually over the shower/tub, it is a two part plastic dome. The top dome is screwed to the RV roof and sealed with DICOR. If undamaged, it should not leak. The interior dome is screwed to the ceiling in the bathroom. There is some open space between the two domes. Usually the RV roof (between the ceiling and the roof surface) is dry and there is no moisture to condense on the top skylight dome. If you're getting condensation, it means there's moisture above the ceiling and below the roof membrane. That may be normal if you have "excess humidity" inside the trailer, it may be abnormal and indicate a leak in the roof with water intrusion into the roof structure that migrates to the skylight dome. Which is it? Hard to tell without some careful inspection.
I'd first suggest you eliminate as much humidity inside the trailer as possible. Turn on the bathroom vent fan, open a window in the opposite end of the trailer, turn on the furnace and let the "air exchange through the vent" help dry out the trailer. Remove the inside skylight dome, do an inspection with a flashlight to see what you can discover. Inspect the entire wall/ceiling surfaces to see if there's any indication of any water damage. Don't forget to open every cupboard and check the wall/ceiling joints inside the cupboards!!!
There should be "very little to no condensation" inside the skylight domes and if there is any, drying the trailer interior "should" eliminate it. If it doesn't I'd play the "be cautious" card and make sure there's nothing leaking on the roof. Better safe than sorry !!!!!
2015 F250 6.7l 4x4
2014 Cougar X Lite 27RKS