S.,
this is a delicate question.
I like how Rebecca put it:
'Daddy' is the one who cares and stays in her life,
loving and OWN.
'Father' is the one who was near you, and this is why the children came to existence.
It is not so very strange in this contemporary life, as when she will be going to daycare or school, there will be about 30% of the kids at least, who have similar situations in families.
If you say the dad who is here right now is your Dad,
AND Eddy is your 'first' dad, or also 'dad',
this will confuse her little mind.
If you divide the situation with distinct words:
here is Your REAL Daddy - he is with US, he is our OWN!
and here is Eddy, he is a Father, who was near me when I was giving you birth...
this will not confuse her, as she will be able to define the difference through the difference of the words.
I believe, Rebecca suggested a win-win situation.
take care, S., all the happy days to you all!