It's important to understand the difference between running more than one application and having more than one window. That said, the sort of parent and child window system you want can be done, but not without some difficulty. The GDK doesn't have any internal commands for creating a new window, so you have to understand and utilize the Windows API.
Attached are a couple tutorials. One is by jinzai, and the other I'm not sure of. (Originally posted
here and
here)
It's a bit of reading, but hopefully that can get the ball rolling for you!
My site, for various stuff that I make.