In general, if a method "foo" is defined by any superclass of a particular $object you can just call $object->foo(). The only reason you would need SUPER::foo is when you've overriding foo in the current package but you still want to call foo in whatever superclass defines it first (update: or last, depending on how you look at it: see perlobj).

As for the fork() question: you can't modify any state in any parent process from a child process directly (update: or vice versa). You'll have to use the same mechanisms that you'd use to communicate between "unrelated" processes, though there are a few methods to simplify setting up the communication between parent and child processes. See perlipc and perlopentut for starters.