I don't even have distant relationship with that place.
You need an "a."
"... a distant relationship."
It could be more natural to say "I don't have even a distant relationship" instead of "I don't even have a..."
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
I'd use 'connection' or 'link' rather than 'relationship'.
Context is always important; labelling is rarely important.