Well, my two call me "Jay" most of the time. The funny thing about this is that sometimes "Mom" slips out at home, and I know that both of them refer to me as their mother at school because their friends come up to met "Mom" after school. Devin actually accepted me as a mother figure first, which was kind of interesting because he was so angry with his biomom for leaving him and not showing up when she said she would. According to him, she was a "liar" (he was 4 at the time, and totally fed up: "she lied to us" was the only thing he said after she failed to show up to pick them up again) and he really never spoke of her again, not at all.
So I thought I might have a bit of a battle there, but hoped it wasn't too late to bond. Well it wasn't - he and I got along straight away and it's been like that ever since. I have no problem calling either one of them "my" kids, because biomom hasn't been involved in person since about June of '07, and hasn't spoken to the children since October of '07.
My stepdaughter, whom I do frequently call my daughter (why not? That's how I feel) is such a sweetheart but since she's older does occasionally talk about her mom. However when she does, she has to make everything up because there's nothing real there to go on. we do mother/daughter things together and she's glad I think to have a mother type figure around, because she's the one who calls me Mom most often.
We share equal roles in discipline and everything else. In some ways that's much easier than the situations some of you are in, because you have to pass everything through the hands of a bioparent who is involved and wants to be there for the children. But in other ways our situation is tricky because of the emotional ramifications of having a child or children who've been totally abandoned by a parent. Then, you have those issues to deal with and they can be hard to get around sometimes, because they're so subtly expressed.
Nevertheless, the kids are no trouble for me. I love being their mom. Heck, I am their mom - you know? I'm not afraid because it's so wonderful to watch them grow up so beautifully after such an ordeal before