If your jukebox is running Windows, you should be able to se that up on your existing network. (I'm assuming you have a router or something on a local network wired/wireless). You should be able to access the drive on your jukebox as a drive on your laptop (f, g or whatever) using windows. You should also be able to use VNC or Remote Desktop Connection (part of XP, might be XP Pro though) to log on and view the screens and run it remotely.
You shouldn't have to have 2 different networks to make it work. At home I have a router connected to cable internet. Then wireless in my house 3 other PC/laptops. There is a printer connected to a desktop. From the laptop I can print to it, access the desktop harddrive or I could log on to it using Remote Desktop Connection and still connect to the router and the internet.
So I'd just throw them all on the same network (local) and access it remotely. You should be able to connect to it by name or by IP.