I would say snag the Burley as my first thought - but let's think for a minute.
You can go here to find out what year the Burley is:
https://burley.com/support/what-year-is-my-burley/
You biggest concerns will be:
1) will the Burley still be enough trailer for your needs in a year or two?
2) what kind of condition is the Burley in? Are the wheel bearings good? Has the frame been damaged? Is the nylon body fabric in good shape?
I used to have one of the original Cannondale Buggers from the 70's. I've had 3 other trailers since that one died. BTW, it didn't have to die, but given that the trailer was 30 years old, Cannondale no longer offered spare parts, and it just wasn't worth making my own parts when I could get other, used trailers (but newer), much cheaper.
So I bought a cheap trailer - about the price range of the InStep. Was NOT all that happy with it as a bike trailer. The wheel axles were going to have wear issues and several other weak points. Nothing you would notice if you were doing weekend rides for a year or two. But I noticed.
I found an early Burley used cheap. Used it until the hitch broke. Used hitch parts from the El Cheapo above to repair the Burley. Then I was gifted a used but serviceable and newer Burley trailer - which is the one I now use when I need one.
The El Cheapo has been repurposed as a canoe hand trailer so I can haul my canoe from the car to water. For this it works well enough.
My point? The good quality of the Burley and Cannondale trailers will see them outlast your need of a trailer, with only a little maintenance and care. With only a little care your children, who are now riding in the trailer, could end up using the same trailer for their children.
The El Cheapos won't do that well.
However, like all used things, try and know a little bit about what you want to buy. If the trailer has been left outdoors in the sun, the nylon fabric could be rotten. Maybe somebody's brother stepped on the frame, and bent it so the wheels don't run true. Or maybe they backed over one of the wheels with their car - and the wheel is trashed, but looks ok if you don't look hard.
A little depends on you, also. If you are going to do 50-milers, or more, with the trailer, you will want the better quality without question. If you are just riding 5 miles for fun, make a stop at the park, and then ride home? El Cheapo may do the job for you.