This display of preference for one parent is very difficult to live through, but it is a normal occurrence, particularly at your son's age. It probably would have happened, at least to a degree, even if you hadn't become pregnant and had another baby. During the second year of life, leaving a child can be very painful whether it's leaving him at child care, at Grandma's house, or to go and have another baby.
Protest is a healthy way for your child to handle separations. As the pregnancy progressed, he may have sensed on some level that you were going to leave him. His way of protesting that separation may have been to spend more time with Daddy. Thank goodness Daddy could be there, obviously not all the time, but at some of the important times anyway.
It's fine to let Dad continue those routines that are working well. When Dad's not around and time allows, you should begin some new routines or try to resume some old ones have some playtime together, read a book before Daddy takes him to bed, do something special when the newborn is sleeping, etc. Keep reminding him that you are there, too, even if he requests Dad.
There will be times when he wants you and you may not be able to immediately meet his needs. When these situations occur, tell your son that you will be with him as soon as you can, and then follow through when you can do what he's asking. And when you do so, remind him that you did. This is the basis of the trust he's looking for that you will return as you did and will continue to do so. This stage also will pass hang in there!