What is the halachic implication when the Ba'al HaBayis ("Man of the House"), as an individual and not the entire community, accepts Shabbos (Sabbath) early? Are his wife and children automatically bound to commence Shabbos at that point or are they able to start at the normal time? Does it make a difference if he accepts it on the condition that his family need not? Does it make a difference if he is absent (i.e. at Shul) but perhaps they are bound when he arrives home? [With sources please :)]
No they are not bound. Even when he arrives home milachah may still be done although not personally for his own benefit.