uploading new contacts with relationships
Welcome to SE!  Yes, you can import the relationship at the same time.  The documentation describes your situation here.
This is based on one row per child with parent details in the columns.  You import once for child, mother, relationship and once for child, father, relationship.
Check that your default dedupe rules work for the parent fields you are importing to avoid duplicates being created.
You don't need to do anything special where more than one child has the same parents other than check the dedupe rules.  Each child is a separate line.
I'd suggest trying this on a test system first to become familiar with the process and check your dedupe rules are working as desired.
Try following the steps in the documentation and let us know if you have further questions.