If I live in a trailer, can I light the menorah by the window of the trailor while it's moving (driving down the highway, lets say) and fulfill the mitzvah of lighting the Chanuka lamp?
In the Sheilos U'Teshuvos of the Maharsham (Rabbi Shalom Mordechai Shvadron) Chelek 4 Siman 146 he writes to a Rabbi in the city of Leipzig the following (my own translation with added clarifications):
To answer your letter from the 2nd day of Chanuka, if it is permissible to light the Chanuka candles on the train - I did not find the matter to be so clear. However we know that someone who pays [for a residence] for the entire night is as though he rented a dwelling place to eat and sleep and is [therefore] obligated to light Chanuka candles.
However Rashi [on Gemara Shabbos 23a d"h 'haroeh' seems to indicate otherwise when he says that] someone on a boat is not obligated to light Chanuka candles [despite the fact that the person has paid money to be on the boat and is as though he has rented a dwelling place for the night]?!
We can say [that Rashi's boat case poses no problem to what I said about the train since] in those days boats were open without walls and the wind would blow and [therefore] a boat could not be classified as a house at all. (In other words, paying money to reside somewhere all night does create an obligation to light Chanuka candles unless there is something about your place of residence that precludes it from being defined as a "house".)
And even though the train does not remain stationary, we don't find anywhere that the "house" needs to be "kavua" (established, or in this case stationary) to be considered a place of residence that would obligate one to light Chanuka candles. The reason being that since the point of the mitzvah is publicizing the miracle and lighting on a moving vehicle does not negate that reason.
Based on this teshuva, it seems clear that one WOULD be obligated to light in their trailer even if it is moving. (In fact, the trailer seems to be an even better case than the train since the person owns the trailer and is not simply renting the place for a night.)