If you read the sticky at the top of the page that is a packing list, that is a good start. You can sort of figure out which items are specific to a trailer and eliminate those.
Having said that, when we tent camped last year a couple of things turned out to be extemely useful.
A plastic, low wattage lamp for inside the tent. Gave a nice warm glowing light.
A couple of outdoor extension cords. One of which goes into the tent, then a power strip is plugged into that, then the lamp and phone charger. Battery charger, too, if you use one for your camera. We used a 5 gallon bucket with lid as a nightstand, and then to put the cords, etc. in for packing.
The other extension cord stayed outside, to plug in the white Christmas lights hung in our EZ up. Makes seeing your site easier, but not blinding. We used an electric tea kettle to make hot water for hot drinks, too.
Other, more experienced travellers can give more advice....
Have a good time--Wish I could join you!