To answer your specific question of "How do you invoke a tKInter event from a separate object", use the event_generate command. It allows you to inject events into the event queue of the root window. Combined with Tk's powerful virtual event mechanism it becomes a handy message passing mechanism.
For example:
from Tkinter import *
def doFoo(*args):
print "Hello, world"
root = Tk()
root.bind("<<Foo>>",doFoo)
# some time later, inject the "<<Foo>>" virtual event at the
# tail of the event queue
root.event_generate("<<Foo>>",when="tail")
Note that the event_generate call will return immediately. It's not clear if that's what you want or not. Generally speaking you don't want an event based program to block waiting for a response to a specific event because it will freeze the GUI.
I'm not sure if this solves your problem though; without seeing your code I'm not sure what your real problem is. I can, for example, access methods of root in the constructor of an object where the root is passed in without the app locking up. This tells me there's something else going on in your code.
Here's an example of successfully accessing methods on a root window from some other object:
class myClass:
def __init__(self,root):
print "root background is %s"%root.cget("background")
root = Tk()
newObj = myClass(root)