Without having reservations we have gotten a site for our 40' motorhome and Jeep in Madison, Bridge Bay and Mammoth campgrounds in the park.
In the Tetons we have stayed at Colter Bay campground (not the RV park next door) and Gros Ventre.
Therefore, I'm sure with a 30' trailer you'd be able to reserve a site in most of their campgrounds, but not all.
We've never reserved so I don't know what the reservation site is like but there might be pictures of the sites and perhaps you could see if there are tree interferences or if the site is wide enough to fit your tow vehicle next to the trailer or angle it across the front of your trailer to fit.
