If the tounge of the trailer is installed with bolts - remove it and replace it with a non-braking tounge (easy fix). Plug the line coming out the back of it with the appropriate cap fitting (hardware store or automotive store probably have what you need, and it's cheap).
If it's not attached with bolts - you will have to get someone to cut it off with a torch and weld a new one on for you.
You can also drill a hole on both sides of the hydraulic braking coupler and insert 1/4"-20 bolts through the pieces that slide. I recommend using 4 bolts (two on each side) if you do that, so that there is enough strength holding it in place. And even then, I'd check it constantly. This is NOT my recommended way of taking care of it though - it's only a cheap suggestion, but not one that I would personally do, as I don't think it's the "right" way of fixing it.
Or... you can figure out why the braking system isn't working, and fix it properly. THAT is my true recommendation. If you need help troubleshooting... let me know.
All the best,
Glenn