You can use one of the VNC server/clients, such as tightvncserver or RealVNC, to give you what amounts to a "Remote Desktop". However, you are going to be constrained by your uplink bitrate and I haven't seen any VNC vendors claiming to also send audio. Of course there are other audio streaming servers. The challenge for you is simply to choose one and figure out how to integrate it into the setup you desire.
As far as what Weaved can offer you, if you can set up some streaming media server that uses TCP and requires port forwarding to enable incoming connections from outside your LAN, then Weaved can help make that happen without port forwarding.