About "smelly" stumps, just a rare possibility:

Two out of my three children had very smelly, indeed raw, cords that did
not fall off until after 6 weeks. There was oozing until 8 weeks. Our
health practitioners thought it was just a "fluke." Can anyone guess what
it really was? Two out of three in the same family? Hint: When each of
these two were teething, there was a lot of bleeding when the teeth
erupted, so much that the dried blood in their mouths looked as if I had
been feeding chocolate to them. (No such luck.) Well, it turned out that
both of them have a severe form of Von Willebrand's Disease (Type III) so
that they bleed from their mouths and mucous membranes. Years ago, girls
who had this disorder were a real puzzle to practitioners because they
looked like odd hemophiliacs, but of course couldn't be because of their
gender.
Looking back after their diagnoses, I remembered the "stinky stumps." When
my grandchildren are born, I will be a nosey grandmother checking those
cords.

Bonny Nothern, IBCLC