Guys, im pretty sure it worked like this.
Shyvana's Biological Dragon Father and Dragon Mother mated in the normal way that Dragons do
Shyvana's mother laid the egg that would become Shyvana when the egg was hatched
This is where it gets tricky because it involves the dragons magical nature and how it interacts with an embryo in an egg
A mage (Maybe Ryze who knows, or knows why) interacts with the egg in a way that causes his own magic to come in contact with the egg
Somehow the egg absorbs the mages magic, and it changes the embryo
Shyvana whos dragon nature makes her deeply affected by magic (and magic inhibitors showing that a dragons biological functions must be very tightly connected to their magic) is affected by the mages magic
Because the magic came from a human, Shyvana's embryo takes on the characteristics of a human
Thus Shyvana is born as part dragon part human,
This must mean that a Dragon's dna (or equivalent) is effected by magic, so when two normal dragons mate it must have something to do with the sharing of their individual magicks.
But Shyvana had a mage's magic mixed in giving her 3 sources of magic instead of two. So its like she has 2 fathers and one mother, but I would consider her dragon father her REAL father...
Did i explain that well enough?