Dzbanecz
nik or dzbanecz
ek ?
we have dzban - jug (rather big one)
diminutive dzban
ek- small jug
diminutive dzbanecz
ek- even smaller jug
that is very literal translation, but then very litte jug seems appropriate if you are talking about wine. - it doesn't feel like what you wanted to describe
"Sięgać/ sięgnąć po kieliszek" - literally - reach for a glass - turn to alcohol in search for relief/ to feel better and so on
"Zaglądać do kieliszka" - look into the glass - if we talk about the problem
Those two expressions do not specify what kind of alcoholic drink it is, but we don't drink beer from "kieliszek"
I would go for 'trunek' - it's not a slang it's a literary word rather but it conveys the meaning you wished for in the first sentence
- I would say trunek means just any alcoholic drink