This looks like what you're looking for:
About FreeRDP-WebConnect
FreeRDP-WebConnect is an open source gateway for accessing RDP sessions using any HTML5 compliant browser. In particular it relies on the Canvas and the WebSockets feature. FreeRDP-WebConnect is a subproject of the FreeRDP project.
On the server side, a standalone daemon - written in C++ - provides a Web page via HTTPS (or HTTP, if configured) and uses FreeRDP libs to connect as a client to any RDP session. The server side WebSockets implementation handles current RFC6455 only, so browsers that implement the older drafts do not work. With RFC6455 being raised to the "Proposed Standard" level, this should change now really soon.
I would create an account on the server for the user, and only give it access to the one application it needs access to.