Third day of Chanukka. Today before sunset we light the fourth candle
Every night we light Chanukka candles after sunset, but today, Friday, we should light the Chanukka candles 20-25 minutes BEFORE sunset: approximately at 4:10 PM (NY time). Why? Because at 4:14 PM we light Shabbat candles (see here), and Chanuka candles must be lit before that.
Another specific rule for Friday's Chanuka candles: while every night the candles should last at least for half an hour, on Friday, the candles should last for more time. So, make sure your candles are long enough, or have enough oil to burn for approximately one extra hour.
When Shabbat is over (after 5:20 PM, NYT), at home you should first recite the Habdala and then you light the Chanukka candles. In the Synagogue, for practical reasons, we should first light the Chanukka candles and then do the Habdala.
When spending Shabbat at your parents /in laws house etc., do you have to light your own candles in your room or at home before you leave?
If you will spend the whole Shabbat at you parents/in laws, once you're at their house, you (spouse, children) are considered part of the extended family of your parents, and since you also partake the same food, boarding, etc. you are included in their Chanukka candle-lighting without further requirements. So, you don't really need to light your own Chanukkia.
However, if you and your family are going to your parents/in laws/relatives house after Shabbat began or for dinner, then you should light Chanukka candles normally at your own house. In this case, it is recommended that you don't leave your house while the candles are lit, to avoid any fire hazard!
Shabbat Shalom and Chanukka Sameach!
Chanukka candle lighting in NY: 4:10 PM
Shabbat candle lighting in NY: 4:14 PM
Shabbat ends in NY: 5:20 PM