Staying with your D until she falls asleep has obviously been going on a long time. I think for whatever reason, your W doesn't WANT to spend quality time with you at the end of the evening or she would be more motivated to assess this situation. This is your first child, both of you. I don't really know, just thoughts. As parents, it is our responsibility to 'work ourselves out of a job'.
Independence is KEY here.
We spend time playing with them all day, we spend time feeding them, we spend time doing things for them. This isn't to say that you desert your child. If you begin letting go when they are born, by allowing children that moment of self-retrieval, then you are ahead of the game and your children are all the more independent for it. I always cuddled and cooed with my babies during the day time when I put them in the 'daybed' for naps, rocking them to sleep and playing with babies, but at night, when I put them into their beds, I kiss them goodnight, pat them on their little buttocks and tell them sweet dreams, as soon as our prayers are said. I used to occasionally stand just outside the door and wait for the steady deep breaths of deep rest, just to assure myself that they fell asleep quickly.