I have pulled two kids in a "home made trailer" many miles behind my Paramount Tandem. My connection point was a threaded 1/4" Heim Joint. I used a safety cable as a backup. The joint never failed after years of use. Today, I would use a 1" nylon safety strap. My home-made trailer had the "high mount" tongue like in your top photo. I have sold many trailers as a bicycle dealer. Starting with Cannondale's in the 1970's that had the "twisty nylon" seat post tongue connector, to the folding Schwinn (imported) trailers that had the frame axle point connection. By far the nicest quality trailers I have ever sold were the Burley's. As expected, they were also the priciest. IMO, they all towed great, I could not see any advantage or disadvantage with either a high or low tongue mounting, they were all stable. If you build a trailer keep the center of gravity low as possible. I would make the trailer no wider than a doorway for storage. My home-made trailer was built for 27" wheels, but I would stay with 20" alloy (36-hole BMX) rims today. You want to select "quality" high pressure tires. Just like towing with a truck, keep in mind that you have to be able to stop and control the Gross Vehicle weight. That's You, the Bicycle, the trailer, AND your cargo load. So you might want to upgrade your braking system. Trailers are like riding tandems. They are slow going uphill. But haul butt going downhill, which is when the braking ability is challenged.
Good luck
John