In America, if you are using company property at home on your personal network and the company tunnels in and scans your home network for "security" reasons, there's not much recourse.
You would have a very difficult time even proving that they did it unless they told you that it happened or if you were the kind of person whom, bordering on certifiable paranoia, kept logs of all of your home internet traffic.
Even then, the only thing you could do would be to sue the company, a very expensive process with no guarantee of success and that would take years to see any small measure of justice. They would only be liable for the damages you suffered as a result of their theoretically justifiable intrusion into your home network unless they tampered with your systems or downloaded files from your other computers, in which case you may have a criminal complaint against your company, but even with the Federal laws (like 18 U.S.C. § 1030 federal computer hacking) you not only have to prove that they accessed your personal computers without your permission but also that they did so with the "intent to cause harm".
If they did this and then fired you because of what they found, then you might have the slimmest of chances with a good lawyer to both federally prosecute the company and also sue for damages, but you first have to keep a flawless and undebatable log of all network activity on your personal network, bring a work computer to your home, join it to your network, and have someone acting in an official capacity from the company (because some rogue I.T. guy poking around doesn't represent the company and would thus be personally liable for the damages, absolving the company of any guilt) use that computer to access your personal network, snoop around, and download your personal files or data AND cause you some verifiable injury for what was found.
To say that is a tall order is such an understatement it's like saying Mar's Mons Olympus is a pretty big pile of dirt.