Let us suppose the family name is [山田]{やまだ}.

Most commonly, we would say:

>「山田[家]{け}」 ← 「家」 is read 「**け**」 for this usage.


>「山田[一家]{いっか}」

***Formally***, we could say:

>「山田[一族]{いちぞく}」

「一族」is not an everyday word.  It could sound too dramatic or theatrical if used in a casual convo.



> "And would you use the same language when talking to a member of the family you're referring to and when talking about that family to a third party?"

The same phrase can be used on both occasions.　

  [![enter image description here][1]][1]  
<sub>(source: [k-img.com](http://image.eiga.k-img.com/images/movie/83447/poster2/200.jpg?1457577317))</sub>  
  [![enter image description here][2]][2]  
<sub>(source: [so-net.ne.jp](http://silvercopen2.c.blog.so-net.ne.jp/_images/blog/_e73/silvercopen2/E382B9E382AFE383AAE383BCE383B3E382B7E383A7E38383E38388EFBC882011-07-142019.01.47EFBC89.png?c=a0))</sub>  
    

   [1]: https://i.sstatic.net/9PqCX.jpg

   [2]: https://i.sstatic.net/zgfaO.png