My baby is almost 3 mths old now and i've got 3 miniature schnauzers at home. Before baby arrived, i was also pressured by my parents to rehome them. How to? They are like my kids. In the end i told my dad that i'll keep the dogs and he can have the baby! haha! Then they finally gave up.
More importantly, the dogs are ok with my baby although i do not let them run around her as she is still so young. And Kayla has gotten used to the barking although she did get shocked intially in the first 2 weeks or so.
If you end up keeping the dog, bring a towel to the hospital to put in the baby crib to absorb the baby smell. Its to give to your dog as a intro to the baby. When you get discharged, let someone else carry the baby when you reach home and be sure to 'sayang' your dog so he will not be jealous.
A colleague taught this to me and it seems to work.
Hope this helps! And hope you get to keep your dear one.