Let us start with your assumption that a woman accepts Shabbat by lighting the candles, and proceed from there. The primary source for that approach is the Behag,[1] who says that one must light Chanuka candles on Friday before Shabbat candles because if the Shabbat candles were lit first, it would then be forbidden to do melacha (actions forbidden on Shabbat), including lighting the Chanuka candles. Several Rishonim[2] disagree and posit that one accepts Shabbat only by davening the Ma’ariv of Shabbat. However, many accept the Behag’s view. The Ran,[3] for one, says that the final warning of the shofar blasts before Shabbat[4] instructed people to light the Shabbat candles. He explains that since this is preferably and usually the last melacha done before Shabbat and is done in Shabbat’s honor, the lighting also serves to usher in Shabbat. The Shulchan Aruch[5] cites both opinions, but the Rama[6] says that the minhag is basically in accordance with the Behag’s stringency.
Another well-known halacha that emerges from this dispute relates to the procedure of lighting. The Rama[7] says that one lights prior to making the beracha on the candles because one accepts Shabbat by reciting the beracha, and it would therefore be forbidden to light the candles subsequent to the beracha.[8] Rav Ovadya Yosef[9] says that the Shulchan Aruch rejects this approach, and thus rules that a Sephardic woman should make the beracha before lighting and that she does not necessarily accept the laws of Shabbat with the lighting. Although he tried to unite the Sephardic communities behind this practice, especially regarding the order of the beracha and the lighting, different customs still exist among Sephardim. In contrast, Ashkenazim accept the Rama’s ruling and basically do no melacha after reciting the beracha following the lighting.
Why do we say that the Rama basically forbids melacha like the Behag? The Behag’s terse statement implies that once the Shabbat candles are lit, no more melacha can be done at all, and, therefore, there is no choice but to light Chanuka candles first. However, others accept his basic approach that lighting ushers in Shabbat, but not in an absolute form. Rishonim[10] cite the Maharam, who says that one can light candles on the condition that the restrictions of Shabbat not take hold immediately, and the Rama accepts this opinion. Others claim that only women who light candles thereby accept Shabbat, whereas men do not accept it when they are the ones to light.[11]
To answer your question, only the woman who lights accepts Shabbat, and this does not affect the rest of the household.[12] In fact, generally, when one person has accepted Shabbat and others have not, the person who accepted Shabbat can ask the others to do work on his or her behalf and can receive direct benefit from it.[13]
Let us conclude by pointing out that a few issues remain in applying the leniencies cited in the previous paragraph. The Magen Avraham[14] says that since not all agree that a stipulation not to accept Shabbat via lighting is effective, a woman should use this idea only in a case of need.[15] His proof is interesting: if it were so simple to delay the acceptance of Shabbat, why would we not make the beracha before lighting (as the general rule is that berachot precede the performance of mitzvot)?[16]