Two internet connections. how to make teamviewer (or similar) work only through one of them?

Question

teamviewer

I repeat with the question, I think I made the wrong heading and the right people passed by.
The initial data, a working computer with ubuntu, the Internet through a proxy and the desire to make yourself a remote control on your own, there is also a 3g modem.
Officially, access is given only to Windows, as a corporate standard, so I want to "play pranks")
I have already connected via teamviewer, as an alternative I consider remote access built into chrome. those. chose the simplest solutions out of the box. But they do not work through the corporate Internet, I tried to register a proxy in the teamviewer, but it did not help.
So I connected via modem. To make teamviewer work, I had to chop off the corp. grid, turn on the 3g network, connected, rejoiced, and then it dawned on me ...
To work remotely, I need a corp. the grid is always, without it my programs will not reach the base.
If you turn it on after connecting to 3g, then the connection is terminated.
I am sure that there is some kind of shamanism to force the application to go only through the "correct" network, and everything else through the corporate one. Tell me please. and I can’t even formulate what exactly I need and how to look for it.