The whole family is used in more formal occasions or written expressions. For example, letters or invitations, we usually use "family" instead of "family". It is customary to use "home" in calligraphy works; However, in general communication, casual occasions or colloquial expressions, we use simple and clear "family".
If you send greeting cards or greetings to leaders or elders, then using "family" can better reflect the respect and solemnity for leaders and elders; However, if the object of blessing is close relatives and friends, but we use "family", it seems too grand and melodramatic, and it is really more appropriate to use "family".