If we are going to be stationary for any period of time (more than a couple of days) I use a bi-pod stabilizer and it makes a very big difference. Without it in place, when Brandy (our dog) gets up and turns around in the middle of the night, it wakes me up because the trailer shakes. Or when one of us walks around, it shakes. With it in place-it is solid. We don't have a Trail-Aire hitch and with them, I understand that the trailer still shakes, even with the stabilizers. Put plenty of tension on the rear stabilizers after the front jacks are set and make sure your wheel chocks are tight should help too.
Good luck,
John