Several issues throughout the forms given in this thread.
Most pressing is the fact that nothlir is likely not a Sindarin word to begin with. It is a 1st Age Mannish word, likely under Sindarin influence or even of Sindarin origin, but not Sindarin. Use noss.
A genitive construction "Home of the Family" would be Bardh-e-Noss or Bardh-i-Noss; note the use of e in the former, rather than en. Alternatives with bâr are also possible of course: Bar-e-Noss, and Bar-i-Noss. However there is no instance in which *bard (without a final h) could work here.
Barnos is correct as a compound meaning "home-family"; however this would likely refer to the family itself, not the building, and therefore not what is required here.
Noss Arthedain (note the double ss!) would mean "(a) family of Arthedain", far too unspecific IMO.
Pen-odhron could work for "orphan, parentless"; it could be incorporated into the name as Bar-i-Phenedhryn "Home of the Parentless-ones" or Bardh-i-Phenedhryn.