Shabbat and Hanukka candles

Every day of Hanukka we light the candles after sunset, but on Friday, we light Hanukka candles earlier, about 20 minutes before sunset. Why? Because 18 minutes before sunset we light Shabbat candles, and Hanukka candles must be lit before lighting Shabbat candles.
There is another important rule for lighting the Hanukka candles on Friday evening: while during every night of Hanukka, candles should last for at least half an hour after they are lit, on Friday, the candles must remain burning for a longer period of time. Therefore, today we must make sure that Hanukka candles have enough oil, or are long enough, to last for about an hour after sunset.
As we already explained, it is also customary to light Hanukka candles in the Synagogue. Today, Friday, we should light the candles in the Synagogue  before sunset (if possible, after Minha). In the synagogue, the berakhot will be recited only if ten or more people are present at the time of lighting the candles. If ten people are NOT present in the Synagogue at that time, we should light the candles without saying any berakha.
When Shabbat is over, in the Synagogue we first light Hanukka candles and then we recite the Habdala, so that the message of the Hanukka candles, promoting publicly the miracle of Hanukka (pirsume nissa) can be witnessed by more people. If we recite Habdala first,  it is possible that many people will leave the synagogue before we light the Hanukka candles. In our homes, however, first we recite the Habdala and then we light Hanukka candles.
If we will be spending Shabbat at our parents, in-laws or friends’ house, do we light our own Hanukka candles at home before leaving, or we light the candles in their house?
1. If I’m are going to spend Shabbat, for example, at my parents’ house (and have dinner and stay to sleep there) my wife, my children and I, will automatically be included in the lighting of the candles of my parents, because we eat and sleep at my parents’ house. In other words, in this case we do not need to light our own candles of Hanukka before we leave our homes. We also do not need to light Hanukka candles in our own room in my parents’ house.
2. Now, if I go with my family to my parents or someone’s home after Shabbat began, for example, if we plan to go to my parents just for Shabbat dinner, then I should light the Hanukka candles normally in my own home with my wife and children.
In this case, it is important not to leave our home while the Hanukka candles are lit, to avoid any serious fire hazard, ח”ו.