A baby sister for Frances by Russel Hoban
Who's That Baby?: New-Baby Songs by Sharon Creech
Shirley's Wonderful Baby by valiska gregory--I didn't love this one but my ds at 2-yrs-old did
There was another one I really liked that I can't remember the name...it had a pattern of presenting some kind of problem about the baby and then the toddler big brother finding something he could do to help. If I figure out the name I'll come back to post.
You could try doing searches (in a library catalog) about siblings rather than new babies so that it isn't just about the arrival of the baby but LIFE with the baby. Children's librarians are also extremely helpful about stuff like that.
About the length of time...it is so hard to say because children that age are difficult anyway. DS was already an extremely hyper, high need child and I didn't notice a huge jump in bad behavior with his new sister. DD1 had a really hard time with DD2 being born and was really quite difficult for a whole year but I don't know how large a factor the new baby was in that.
She would have days and weeks in which she would cry ALL THE TIME unless I was holding her and reading her a book. So you have my sympathy. She liked the baby though. And she liked the attention I gave her when she was holding the baby and being gentle. The other thing that helped a lot was when we had extended family around and an aunt or uncle or grandparent would be willing to sit with her one on one for an hour or more and read every single book she produced. She loved that.
