A cycle of dishonesty with your children about their father has been created and perpetuated. With all due respect I think truth was in order from the very beginning. You never have to cover for the truth, you never have to remember the truth, and young children can handle the truth.
This is your opportunity to come clean and allow your children the dignity of seeing their world as it really is.
Please understand I know where you are coming from. My daughter was three when her mom began drinking uncontrollably. I lied to her a lot and in retrospect it was a big mistake. Please also understand I'm not attacking you or your prior decisions. You did what you thought was right at the time, and with your daughter's best interests at heart.
What I am saying is to apply what you know now, include the truth of today and of the past, and create a culture of truth as the norm for the remainder of your daughter's life. I strongly disagree with lying to children, at any age, about addictions in their parents or most anything else. I think, in the long run, it does more harm than good.
My two cents.
Cyranoak