If you're that keen a cyclist you'll get your money back on the investment, Wike, Burleigh, Dolphin, all sorts, that convert nicely to buggies. Definitely look on Ebay.
Conversion to buggy is never all that great, anyway, I found (we have a Chariot, btw).
Sorry to be graphic, but I had the same concerns 11 yrs ago & concluded all this:
Trailers are small & lightweight. Unless they are hit by something large with high ground clearance (think landrover with bullbars, or Artic) then upon impact they will fly up in the air. So what you want is that the trailer comes with a good belt system for restraint & is sound enough structurally to take being flung about a bit without collapsing in on itself (there's not much you can do about the damage from impact and being crushed under a high clearance/large truck, but that applies if you drive a micra or mini, too).
Most trailers will take the impact well enough, the lightweight ones (like Chariot) are engineered to be strong, and the heavy cheap ones are made of steel, plus they won't get flung that far. So the quality of belts is the main thing to examine, look for 5 point harness ideally.
The trailer manufacturers also advise that children wear helmets while riding inside the trailer itself, which I found impractical, but ymmv.
Of course best tactic is to have a big flag for visibility (I sometimes remember mine) & your wits around you so you avoid trouble in first place. Since the trailer is attached to your bike you'll get flung about, too, after possible impact.
You falling off while towing is only bad in that it's quite embarrassing, your kids will simply look on comfortably, probably in bemusement.
We've been towing trailers for over a decade, different parts of UK, & never had one even bumped by any motor vehicles (only fallen myself a handful of times, too, and never because of motor vehicles, either).
There are other guidelines, I wish we had gone for solid rather than fabric bottom, and better waterproofing.