I'm going to agree with Rick on this one. hog family, I salute your steadfast beliefs and what you are trying to do here, but I feel you're opening a whole can of worms that at best should remain closed. By adopting this child, you will forever be tied to this women that it seems you despise. In the past, courts have ruled that limited visitation, pictures, communication, etc is a reasonable request of the birth parents. By taking her child, you will also be taking this woman into your lives, and from your very brief description, that's not something you want to happen.
Also, this is her decision. I know you 2 are trying to help this woman do what's best, but you're trying to get her to do what's best in your eyes and what you believe God wants her to do. Are you really giving her advice on what would be best for her? Perhaps there's more to consider then "she just doesn't want the baby". Maybe the father is abusive, maybe she's a drug addict, perhaps she uninsured. As I applaud your undying determination to have people do what's right, I do think it's a bit selfish to not consider that there's more to the story then meets the eye.
I think the decision can be much more then just not wanting a child. Take the following scenario. A women has no insurance. She already has 1 child she's supporting. There's no way she can keep the baby. Say she gives the baby up for adoption. She now has $10,000 in hospital bills for her and the infant. She's uninsured and has to pay this sum by taking food out of her current baby's mouth. However, with an abortion, she's out $150, and is not destroying the life of her current child.
I don't know, things like this are just too complicated to be black and white. Good luck to both of you and to the woman who has a very tough decision to make.