I work from home and use a work laptop with VPN connection. If I have a personal computer hooked up to the same wireless connection as my work computer (not on VPN though, BUT on a router provided by work), can they monitor what I am doing on my personal computer?
If they have control of the router that you are using, there is the possibility that they are watching every bit of network traffic that any device connected to it is sending and receiving. The VPN is not a factor in this equation at all*. The bigger matter is the work-provided router.
Note that they cannot see what applications you are using. For instance, if you are editing a Word document, they won't be able to see that. They will only theoretically be able to see what websites and other traffic that a connected device is accessing.
The better option would be to ask them outright if they are monitoring everything at the router level.
*Note that you can pretty much guarantee that the work computer is being monitored. I'm not saying that the VPN connection can be disregarded. I'm saying that, as far as any non-work devices are concerned gaining network access by using the work-provided router comes with the possibility that all network traffic generated or received by any device is monitored.
On a related note, since you are using the work provided router for everything web related you are doing on your personal computer, they may very well have a claim on everything you do on that computer as well since you are using their resource (router) to do it.
If you would like to keep your stuff private, or have an interest in keeping rights in work you do for yourself, don't use their equipment for it at all.