This kinda happened to me, except I don't really remember anyone ever mentioning it in front of me. My dad's mom divorced when he and his sister were very small and she remarried, and her husband adopted my dad and his sister, then they had another son. I always knew my uncle didn't look as much like my dad and sister as they did like each other, but didn't know why. My "grandfather" loved us and never treated us any differently than his "real" grandchildren in any way, and never treated my dad differently than his brother. I found out about all this when I was in my 20's. At that point I was curious about my birth family, and I still am now in my forties, but I know that my grandfather is the man I knew all my life and the other man is more of a curiousity, though I sometimes wonder about his other children and who my cousins might be. I did feel slightly weird about the whole thing when I first found out about it, but it explained a lot about things I'd never understood, like why my dad hates his middle name (which is a family name from his birth father's family.) My father has never talked about this with me even now, and my grandmother said that he has refused to have contact with his half-siblings when they have tried to find him, so obviously he really resents his birth father.
I don't think it's a problem for you not to mention it until it comes up naturally for some reason. Then if they ask why you never told them, just say that you love Mammaw very much, that she raised you and is your mother, and that since you don't see your birth mother, she isn't very important in your lives. I also think that it might be easier for them to find this out when they're older, even adults, because as small children they might worry that if your mother left you, you might leave them. As adults or even older teens, they're better able to understand that people make selfish choices that have nothing to do with them. But if it comes up, I'd just be really casual.
BIGGEST ADVISE--quit dissing your birth mother. You may resent her, but your kids are gonna hear again and you'll have to deal with the fallout. And if you say things to other people, sooner or later someone will mention it to the kids. I'd just not talk about her at all. And I'd be careful of passing along your resentment to the kids when you do tell them, because since she has no relationship with them, it's not their fight, and they don't need to be drawn into it. When they're older, they need her medical info and basic family into, but they don't have to hate her becuase you do. They just need to be reminded to respect the feelings of their real grandmother, who has been there loving them all these years.