Pup1 came first so has had hers already (her first one at least) pup 2 has hers today.
Pup1 has NEVER been left at home alone before (she is 9.5 weeks) and since her littermate sister came to us shes never been alone fullstop as they sleep together.
I think they are still very young to be left alone but DH says they have to get used to be apart (why?? they nver are?!)
We have to walk there and so the pups sit ontop of the buggy as they cannot be walked until 2nd injections are done so might be a bit tricky havng them both up there, though they are very docile puggies and will probably slep the whole time!!
I would leave pup1 at home. It is not really ideal to take her into the surgery unnecessarily when she has not yet completed her vaccination course. She will most likely sleep while you are out, but it definitely won't do her any harm even if she doesn't. Do you have a crate where she feels nice and safe?
You will need to make the pups independent of each other. They should get used to being apart from each other. You have your hands full with two pups! You should spend time each day with the pups on your own or else you will find that they have more fun with each other and will never accept you are the leader of the pack. If you let them play exclusively with each other and not individually with you they will see you as no fun and that will make it much harder for you to train them.
The problems will occur when the dogs are a few months old if they have been allowed to be a pack with themselves and the adults in the family are not included.
When the pups are ready to be walked I would strongly advise that they are walked separately so that you can give correct training and bonding with each individualy dog. You have a busy few years ahead of you good luck.