That's certainly an interesting question! Other than braking causing jack-knifing, your other scenario of going around a curve and have it slide out and pull you over seems valid to me. Ideally you could fit brakes on the trailer wheels and use it to do all the braking. (Check out tandem hardware for cable connections, as some tandems have frame connectors to break them down for travel.)
Your best bet might be to just make a trial run with a kid-equivalent weight and see how it handles.