Oh you're using the old old version of the gateway.js script which just allowed hardcoded nodes like the garagemote and switchmotes...
Well the fundamental problem is you cannot send requests from unauthorized clients. That's one of the main points behind this architecture, not allowing random unauthorized requests to open your garage or turn lights on.
If you disable HTTP_AUTH then you might be able to do it, I am not really sure how you can on that old version of the code.
Try watching what happens when you click the button in your browser, if there's any wrappers around the request, I think it will be a websocket request.