The question of finding a trailer with a strong frame is really a good one. Having been looking around recently at new trailers I only found Northwood Manufacturing to have trailers without Lippert (LCI) materials and frames. They build Nash and Arctic Fox (Desert Fox) and few others. They also build their frames and structure to handle driving off-road, and I can't recall any others making the same claim. That speaks to the high quality of their construction. There may be others out there, but I haven't seen them yet. I also haven't seen anything yet by Lippert that yet impressed me, and have friends that had suspension, construction and frame issues on Lippert built materials.
Of course, as Lippert is quick to point out, they build their products to meet the specifications of the manufacturer that requests them. So, if a manufacturer orders a frame from them with lower quality specifications that is what they get. The opposite is also true, that if ordered with higher quality specifications that is what the manufacturer gets also. In defense of Lippert, they are also at the mercy of those manufacturers who install their products.
Regardless of who makes the trailer, check out the build quality of what you are considering. You also might find that there are some manufacturers with excellent build quality, using LCI products.
To find if the trailer you are considering can do as intended you can always contact the manufacturer directly and ask. Remember that you usually get what you pay for, so make your money count as they usually want alot of it.
This is of course, in my opinion.