Need to Set Up RDSL Connection Remotely

Job Description

Need help setting up an RDSL connection on a remote computer with one click IP changing.

I live in one country and have access to a computer in another country.

Project is to create a remote DSL setup, giving me desktop access (team viewer or built in windows rdc or similar) to the remote machine so I can access it from my location.

Then, setup a one click script for changing the machine's external IP. Needs to be done so the remote desktop session does not break. The IP needs to change in a few seconds.

Final output: I log in to remote machine and am able to switch IPs at will.

Current remote machine changes IPs if modem (router?) is unplugged, so the ISP has dynamic IPs issued.

Just to clarify, the desired outcome is the ability to change my external connection's IP to the Internet m).