Same thing happened to my Mom's dog too. She came early & we were on the phone talking with vet or vet asst the whole time. The first pup was stuck in the canal & when we got to the vet the one sac was out a little and went from black to clear. Didn't know if that pup would make it. They did a c-section & all 4 pups lived. We bottle fed them at first as well. Since this was her first litter & she didn't see the pups born it took about 45 minutes for her to start nursing the pups when she was allowed to. Once she started nursing mother nature kicked in with her & pups & she started taking care of them.
I'm sorry you lost one but happy you have 3 precious new ones! Congratulations! I know you and Mom are tired. Praying she will be able to feed her babies.
HAPPY BIRTHDAY!