Generally, there are a couple of wood screws through the base of the recliner and into the slide floor, or into the floor of the trailer if the recliner is not located in a slide. They are fairly short screws so that they don't go all the way through the floor.
Here's another thought though, if you can reach the receptacle, even if it's difficult to get to, and plug in a Power strip with a cord long enough to be able to reach easily, that might be the way to go. Most of those power strips will have surge suppression built into them and could help protect the laptop. I'm not familiar with your particular trailer, so just offering up some generic answers here.