Just tell her this is her brother. He is. Don't say he is a 'half' brother. Too abstract for her. Just say he is her brother. No need to get technical about it...yet.
SO sad, her Mom told her those hurtful things to her, about the baby.
No polite words I can say here... to express that.
Tell her, the Doctor will help baby come out.
Tell her, due to her age/maturity about it all... that baby got there due to.... ? I don't know. My daughter was 3, when I was pregnant with my 2nd child but she didn't ask that to my memory. I just told her, that Mommy and Daddy made her brother because we love each other.
I would also, incorporate her INTO your pregnancy/her baby brother. Now, before he is actually born. I did that with my daughter, and she totally BONDED with her baby brother even while still in my tummy.
We took photos of her with my tummy, she sang to him, talked to him... I told her her baby brother loves her.... etc. I told her that she is special... and Mommy loves her so much... that she is my 'first' baby, always.
Once my son was born, she loved him so much, already.... because I prepped her about it, BEFORE he was born.
"My" pregnancy, to me, was not about 'me'... but rather... a whole 9 months of being so that I could prep my Daughter about her baby brother... and get adapted to it ALL... BEFORE her baby brother came home. THIS made all the difference in how she handled the whole thing and how she 'viewed' her baby brother, in my tummy and once he was born.
Per her age and maturity, I would not get all graphic with her about explaining 'how' you got pregnant..... she is already so confused about accepting the pregnancy and emotionally... she is having a hard time, already.