For Kid's trailers, I much prefer a wrap-around frame design like the old Burley Trailers.
I think it allows a strong, lightweight trailer that uses standard quick-release (or bolt-on) wheels.
It also somewhat isolates the wheels from bumping into stuff.
If you do decide to use the one-sided trailer or trike wheels as above, I'd encourage using a full width solid axle.
My "Heavy Hauler" has wheels with coaster-brakes from kid's bikes. I had originally intended to design surge brakes for the hitch (like many boat trailers use), but never got around to hooking that up. I have seen someone who has done it.
My belief is that if one is riding mostly flat land, and only human powered, that one can generally stop if one's careful. You'll need much better brakes if you are doing electric powered.