We have seen pictures of Dana, SW and the new baby together. One was posted just the other day of them. Meaning that SW and Dana were together after the baby was born. Granted it may have been taken at the hospital but something about it makes me think it was taken at Dana's home. I don't remember which thread it was on or who posted it. If whoever posted first posted it again maybe someone with better eyes or better skills could try to blow it up to see details in the background to determine where it was taken.
But in my opinion, given the hostility between Hannah and Jake, I do not think she dropped SW off a week earlier. A week was enough time to get to AK with her. In fact we have heard that Hannah was not allowing Jake to see SW at all. But then, according to Jake, she suddenly has a change of heart and gives him an entire week with SW. Also according to him (first story) he showed up a day earlier for his weekend and she just let him take SW after not allowing him to see the child at all? I don't think so. Once that kind of hostility starts, it usually escalates, to the point that Hannah would have rather left her with the local sex offender rather than let Jake take her.
Too many other babysitters if Hannah didn't feel like taking care of her. Lenny, His wife, Hanna G, Chris Jr, numerous aunts uncles and cousins.
We know how Jake treated Hannah but we don't know what Jake's treatment of SW was either. Could be why she finally left him.
JMO