Calling base class method after child class __init__ from base class __init__?

This is a feature I miss in several languages and wonder if anyone has any idea how it can be done in Python.

The idea is that I have a base class:

class Base(object):
    def __init__(self):
        self.my_data = 0
    def my_rebind_function(self):
        pass

and a derived class:

class Child(Base):
    def __init__(self):
        super().__init__(self)
        # Do some stuff here
        self.my_rebind_function() # <==== This is the line I want to get rid of
    def my_rebind_function(self):
        # Do stuff with self.my_data

As can be seen above, I have a rebound function which I want called after the Child.__init__ has done its job. And I want this done for all inherited classes, so it would be great if it was performed by the base class, so I do not have to retype that line in every child class.

It would be nice if the language had a function like __finally__, operating similar to how it operates with exceptions. That is, it should run after all __init__-functions (of all derived classes) have been run, that would be great. So the call order would be something like:

Base1.__init__()
...
BaseN.__init__()
LeafChild.__init__()
LeafChild.__finally__()
BaseN.__finally__()
...
Base1.__finally__()

And then object construction is finished. This is also kind of similar to unit testing with setup, run and teardown functions.