Hi N.,
I'm sorry that you are in such a difficult situation. If I may, I'd like to add a bit as an outsider that may be difficult to see when you are on the inside.
First, transitions are hard for EVERY kid! They just don't like change because its hard to understand. At that age my son cried when dropped off at day care even though he was always playing happily when I came back in the afternoon and sometimes didn't want to leave! Since he has been used to being with Mom most of the time, leaving her is going to be hard whether for the week, the weekend or the afternoon.
Second, the birth of a new sibiling is really hard for kids! Especially for a kid under two who doesn't know what's going on,all he knows is this new baby is taking time from his mommy. If I may be so bold, I'd say that the bottle use and constant need to be held is about a new baby in the house, not a custody arrangment, but with the two things together, he may think he's being sent away to make room for the baby!
Finally, young children look to their parents (especially mom) for the correct emotion in a situation. They trust their mothers and believe that if mom feels good about it, it's good. Likewise, if mom is worried, angry or sad, it's a bad situation.
Now a piece of advice: Try really getting on board with the new custody arrangment. You and your daughter should sit down with your grandson and explain very clearly that you love him and his father and other grandma love him too. Make sure he knows that you are happy for him to spend time with his Daddy and that you can't wait to hear about all the fun things he did during the week. Tell him that you and his mom will miss him very much and look forward to seeing him at the end of the week. Then, above all, you must find a way to be happy about his drop-offs. If you are uneasy, he will be uneasy, it's as simple as that.
Good luck with everything. Shared custody is never easy for anyone, but as adults we have to try and make it more manageable for the children.
HTH,
T.