Using Remote Access From Home: Can Work See My History?

My wife is at a job where it is very abusive and contentious, and recently they decided to not renew her contract because she didn't play by insane and illogical rules. It is all a big joke, they are offering severance in a hope that she keeps her mouth shut about what's been going on in the organization. I no longer want her to be subjected to the stress, anxiety, and bullying she's faced for almost a year. I told her to work via remote access, which I assume is a VPN, and get away from their craziness. I'm concerned that her work could hack into her system from the remote access and learn of all of the history of our personal network. Obviously we have searched about things surrounding this type of workplace, influential members of the organization, lawyers, yada, yada, yada. So what is the most they can track? From where can it be tracked--the computer hooked up to the network? Could I hide my IP and make it even more difficult to track. Etc, etc, etc.

Thank you in advance for the crash course in this particular area. I really want to get my wife out of there and have her home, relaxing, and, quite possibly, drinking her guts out until the severance starts rolling in. Thanks, cheers!

Your wifes company could not access your local network but they could monitor connections to the company network. I see no reason to use a proxy to hide your IP address and a number why you should not. The problem with using a proxy server is that it attracts attention to the user, that they might have something to hide. The company would not know your IP address but they would know the identity of the logged in user from the login credentials. Seems to me this is the opposite of what you want.