rreload.py

from importlib import reload
from types import ModuleType

def rreload(module):
    """Recursively reload a module and all its submodules.
    Graph DFS strategy modified from
    https://stackoverflow.com/questions/15506971/recursive-version-of-reload
    """
    visited = set()
    def visit(m):
        if m in visited:
            return
        visited.add(m)
        reload(module)
        for attribute_name in dir(m):
            attribute = getattr(m, attribute_name)
            if type(attribute) is ModuleType:
                visit(attribute)
    visit(module)

Had to change line 14 from reload(module) to reload(m)

Line 14 is in the wrong place, we want to visit (and reload) child nodes before reloading the current node.
Incorporating @dtasev's changes, this is the correct algorithm:

def rreload(module):
    """Recursively reload a module and all its submodules.
    Graph DFS strategy modified from
    https://stackoverflow.com/questions/15506971/recursive-version-of-reload
    """
    from types import ModuleType
    visited = set()

    def visit(m):
        if m in visited:
            return
        visited.add(m)
        for attribute_name in dir(m):
            attribute = getattr(m, attribute_name)
            if type(attribute) is ModuleType:
                visit(attribute)
        reload(m)
    visit(module)