Does the father have to stay away from his baby guinea pigs?

Yes,he should be separated from the mother as well as the babies because he can cause serious problems to the babies such as pregnant among baby Guinea Pigs,injuries,etc.

When the babies are at two weeks old,you should distinguish between male and female baby Guinea Pigs and separate the male baby Guinea Pigs from the females.You can put the male babies with their father and the baby females with their mother.