Surgery in dogs.
I would strongly advice to request your vet to have blood (plasma) ready if you intend to do any kind of surgery. After surgery is done look at your dog closely and check color of gums. They should not be to pale. If gums are getting white call the vet immediately because there could be internal bleeding. If your vet has blood ready they can do a transfusion and save your dogs life.
While a dog can be spayed during a c-section unless there is a problem with the uterus at that time it is not advisable. For one thing her milk will dry up very fast and you will have to bottle feed.
Another risk is that the vessels are so swollen at this time that it can be dangerous and lead to internal bleeding.
While it seems like a good time to do the spay, your dog will have a much harder recovery also.
Talk to your vet about it but I would wait until the puppies were weaned and her milk dried up before she is spayed. The dog and the vet will both have a much easier time of it then.