I would recommend using boxes for your panes. Start with a horizonatal Box that will essentially act as your main window:
hboxMain = Gtk.Box(orientation=Gtk.Orientation.HORIZONTAL, spacing=1)
then two vertical boxes for your panes:
vbox0 = Gtk.Box(orientation=Gtk.Orientation.VERTICAL, spacing=1)
vbox1 = Gtk.Box(orientation=Gtk.Orientation.VERTICAL, spacing=1)
then add whatever buttons you like to your panes:
btn0 = Gtk.Button()
btn1 = Gtk.Button()
btn2 = Gtk.Button()
vbox0.pack_start(btn0, False, False, 1)
vbox0.pack_start(btn1, False, False, 1)
vbox0.pack_start(btn2, False, False, 1)
(with a VERTICAL Box, pack_start will add the child widget you specify (btnN above) to the top of the box, and continue down as you keep calling pack_start. HORIZONTAL will go left to right.)
Then finally add your vertical boxes to the main horizontal box, and ultimately add the horizontal box to your main window.
hboxMain.pack_start(vbox0, False, False, 1)
hboxMain.pack_start(vbox1, False, False, 1)
win = Gtk.Window(title="Home")
win.add(hboxMain)
win.show_all()
It sounds like you want to add window widgets to the right-hand box. I can t answer if that is possible as I assume Window is more regarded as a higher level Container. I imagine it would make more sense to pack into the right side box some text boxes, etc. Not sure why you would want to add a Window widget. Go ahead and give it a try.