Sure. You could replace the DPDT switch with a DPDT relay. However, you'd probably be leaving the relay energized for extended periods of time, which might not be ideal. So, a more reliable, but more expensive/complicated solution would be to use a purpose-built projector screen controller (assuming you are driving a motor of similar size).
Edit: (in response to your edit)
You can still use a relay or a dedicated motor controller, but if you want wireless control, it's really too broad of a question. There are scads of RF solutions and loads of IR solutions. Selecting a wireless control solution is very application-specific.
That said, it seems like your application is very similar to project screen motor control, and there are COTS solutions for IR project screen motor control. You buy a nice little box that switches AC safely, and it comes with a cute little IR remote.