If your desktop and laptop were both running OS X / Linux / BSD, I'd suggest running this on your desktop:
autossh -R 127.0.0.1:3389:127.0.0.1:3389 your.ec2.instance
and this on your laptop:
ssh -L 127.0.0.1:3389:127.0.0.1:3389 your.ec2.instance
You'd then be able to open an rdp connection to localhost on your laptop, and it would be forwarded to your desktop. You shouldn't need to do any additional configuration on your ec2 instance. I'm assuming you don't have an RDP server running on your laptop.
So how do we do this using Putty? (I'm guessing slightly here.)
- select the "Connection → SSH → Tunnels" category in the left hand pane
- for "Source port" enter "3389"
- for "Destination" enter "127.0.0.1:3389"
- select "Local" (for the connection from your laptop) or "Remote" (for the connection from your desktop)
- click "Add"
- you will then want to save these details in the "Session" category
Ideally you will want the connection from your desktop to restart if it breaks for some reason. (If your home internet is anything like mine, it will glitch out and drop connections occasionally. But perhaps your home internet is more reliable than mine.)