Generally, any software which could do what you want is possibly a dangerous thing - I would not want my PC being accessed and my movements emulated by a third party!
Any machine with access to the internet is potentially online at any point (regardless of a surfing - for example, software updates, email clients checking for new email).
Normally to use another persons computer means you'll have to know their password. I would not want to hand over my password to anyone. Or you could create a guest account on each PC (depending on how many PC's there are) with a unique password to you.
This entire question also assumes that the local machine's IP is being tracked - if so, are all your PC's on a static IP?
However, to keep their IP address you could use a program like LogMeIn or TeamViewer or GoToMyPc. From this, you can also save each computer (with username/password) and so access to all the PC's will be fast (and some programs will allow multiple connections).
The remote desktop software examples above are typically computer software packages for remote control, desktop sharing, online meetings, web conferencing and file transfer between computers. This style of software can operate on Microsoft Windows, OS X, Linux, and in some cases iOS and Android.