I personally would use "proche" for family members. It is the most commmon and I feel sure saying it, as I'm not a native! "entretenir des relations étroites" I would use for a community, for a collaboration on something (ex between companies, countries), and also for concept not involving people (two philosophical ideas). Any confirmation natives?
I am not sure of the context so I don't know what would be best in your case.
R.