I'm currently experiencing the same problem and I don't know what's causing it either, but I do happen to have some mods that might have something to do with it, though I'm not sure if they are causing it. These are the mods:

1) Arissa – Wondering Rogue
2 & 3) Towns and Villages Enhanced: Inns & Enhanced Cities: Jarl's House
4) Better Towns Textures

I'm not sure if they have anything to do with the barn door not appearing, but at the same time time I don't know if any of them could be the cause of it. Could someone provide a solution to this problem? Are the mods I mentioned above somehow causing it, and if so, which one(s) could be affecting Dead Man's Drink in Falkreath?

I have the same problem ,theres a frame where the door should be but not the actual door and i have the Ehanced Towns And Cities mod

probably the easiest way to figure this problem out is uninstall the mods that might be conflicting.

did that even used saveTool and Tes5edit and BOSS and no change

I believe it's the Enhanced Towns And Cities mod that's doing this, I'm afraid.

But if you want to fix this solution you can download the Moonpath to Elsweyer mod on the Nexus using NMM, and it puts all the NPC's in the Inn and the carriage is just behind the bar. You might have a stack of barrels in front of the door to the carriage, to fix this just console command the barrel and type "disable" and it should disappear. LOL.

its not Enhanced Towns And Cities mod cause i've uninstalled that and tried this mod and same thing

Actually, the problem IS "Enhanced Towns And Cities - Inns". You shoul uninstall both "ETA" and "Elsweyr", than reinstall Elsweyr. It's helped. But these khadjits in the tavern are the ugliest khadjiits i ever saw!!

i did that and used savetool and tes5edit and BOSS ,still the same problem

anybody know the id for the door

thats what im trying to find using tes5dit and creationkit still no luck

I'd recommend uninstalling any mods that conflicted with dead mans drink, then ununstall and reinstall elsweyr.

i did exactly that and used BOSS and SaveTool not to mention completly uninstalling skyrim and reinstalled and still not working

go to your data fikes turn it on there.your data files are above tech support and below options.this is in your main game file not your nexus mods....this my help

Im having the opposite problem. i went through the door and got on the caravan, but when i travel back to skyrim and get put in the room with the caravan i cant get back into skyrim.

if we are talking about the same caravan , the your system is messed up.you should have no problem getting back to skyrim.i would reload.