Generally, in a public place, such as a hotel, a hospital or similar, it isn’t possible, for valid safety concerns, to light candles in the private room where one is staying.

Therefore, one who finds themselves in such a place, should turn on the light/lamp in their room with intent that this should be in place of the Shabbat candles in their room, and then they should go and light the candles in the designated room, preferably the public dining room where the meal will take place. (If the only area given to light is the lobby or another area where no meal will take place, ideally, it is best to try and eat something near the candles. Ruling of Rav Nissim Karelitz Shlita)

Regarding the bracha on the candles in this case, the prevalent minhag amongst Ashkenazim is to recite a bracha, whereas Sephardim do not recite a bracha, rather they can listen to an Ashkenazi woman’s bracha and will thus be exempted for their own lighting. (See Sefer Ohr HaNer page 30 footnote 90 for a lengthy dialogue about this)

The prevalent minhag is for a woman to light candles wherever she happens to be for Shabbat, even if she isn’t in her own home.
The above is the case even if her husband or other household members remained home and are lighting candles there.
It is, however, ideal in situations where her husband or another household member will be lighting in her home when she is away, to have specific intent, when lighting where she is, not to be exempted from the obligation to light candles via their lighting. (Ruling of HaRav Nisim Karelitz Shlita quoted in Sefer Ohr HeNer Page 34)

The minhag used to be that the first Shabbat after giving birth to a child, a woman would not light the candles but rather have her husband do so. (See Mishna Berura Siman 263:11)

However, nowadays most women do in fact light the Shabbat candles themselves the first Shabbat after giving birth, as due to the advancement of modern medicine and the modern birthing procedures, most women are back on their feet shortly after giving birth, and can light in the room where the seudah will take place and also be present themselves at the meal. (See Shu”t Az Nidberu Vol. 11 Siman 2. This is also the ruling of HaRav Shlomo Zalman Auerbach zt”l and many other contemporary poskim.)
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