Repetition Repetition

Naming

Universally, names of classes are written in PascalCase, and you should really stick to it, even if the compiler does not enforce it:

binary_tree -> BinaryTree

getters

Getters are highly frowned upon in Python. Values are generally accessed directly.

If you really do not want the user to access values directly you may make them "private" by prefixing __ and letting a @property return them.

Decide for your nil values

None is the standard nil (nothing) value in Python but in get_right_height you return -1 if the value isNone. If so just make the default -1 and remove the getter as suggested above.

Repetition Repetition

You repeat b.add 6 times, use a loop to avoid such waste.

No, it is not correct:

set_height is not run due to the lack of parenthesis, hence the height is not correctly set.

Bug

No, it is not correct:

set_height is not run due to the lack of parenthesis, hence the height is not correctly set.

Swapping

In many places such as for example:

    temp = self
    self = self.right
    self.right = temp
    self.right.set_height
    self.set_height

You are swapping values in an obfuscated manner, just use the built-in a, b = b, a syntax:

>>> a, b = 1, 2
>>> a, b = b, a
>>> a, b
(2, 1)

Repetition Repetition

There must be a way to avoid repetition in the below code-blocks, the problem is that you have duplicate functions for left and right, maybe a single rotate function could help you here.

        '''Adding to left subtree'''
        if self.left is None:
            self.left = Node(data)
        else:
            self.left.add_node(data)
            if ( self.get_left_height() - self.get_right_height() == 2):
                ''' Then we need to balance a subtree'''
                print("Rebalancing after inserting", data)
                if (data < self.left.data):
                    self.rotate_left()
                else:
                    self.double_rotate_left()

        '''Adding to right subtree'''
        if self.right is None:
            self.right = Node(data)
        else:
            self.right.add_node(data)
            if ( self.get_right_height() - self.get_left_height() == 2):
                ''' Then we need to balance a subtree'''
                print("Rebalancing after inserting", data)
                if (data < self.right.data):
                    self.rotate_right()
                else:
                    self.double_rotate_right()