Can we connect a U-Haul trailer to the back of a car and have a Sukkah there. Can we go into that on Shabbos or Yom Tov?
Yes, you would be able to use it on Shabbos and Yom Tov as long as that it doesn’t activate any lights or sensors.
However, doing this would require you to make a Eruv Chatzeiros to permit carrying to and from the Sukkah on Shabbos (unless there is a Eruv already in place in your area).
The Sukkah must be parked in a spot which you have permission to park and in a location that will not inflict damage upon your neighbors — by blocking their windows, for example.
Furthermore, the Sukkah must be constructed in a location and manner in which you would feel comfortable to eat, drink and sleep (although not our custom) in the Sukkah.
ראה בלוח יומי תשרי ח”ב בתחילתו וש”נ.