OK, I'm the SM, DH is the BD.
Make the long story short, we kicked SD(almost 18) and her baby out of our house 3 months ago. She lied and disrespected us by back talking, tried sneaking out of the house and got caught when we told her previously it would not be tolerated. This was not the first time we tried to help her with the baby. Before the baby came in the picture, she was not in our care nor visited us.
I've tried to keep contact with SD for the baby's sake after kicking her out. Not very successful since she does not change her lying behavior. I've confronted her about lying and it went no where because she convinced herself her lie is the fact. To me it's very frustrating as I take lying very seriously.

DH does not want to have any contact with SD anymore since he went through SD's behavior while she lived with us. DH does not answer her text or phone calls. She calls only when she needs money or car needs repair(DH's a mechanic).
I am thinking about stop trying since I'm only the SM and what SD seeks obviously is not me, it's her dad. If DH does not want to have the relationship, why should I keep on trying?

I guess I'm seeking reassurance or reasoning for me to stop trying.
I still resent what she said/did to us while she lived here. She never apologized and of course I know I won't get one, at least not any time soon.
I just want to know what is the good reason for me to try at all?! To me, SD is not my responsibility and definitely not my job to maintain the relationship.