The way to dup a file handle is to use the open NEWHANDLE ">&OLDHANDLE"; form. Or the open NEWHANDLE ">$=$fd" form. If you have a copy of the Camel book look under open.

In your case I would guess that the code to use would be:

pipe READ, WRITE;
my $child1 = fork();
unless ($child1) 
  {
    open STDOUT ">&WRITE";
    exec ('cat', $0);
  }

my $child2 = fork ();
unless ($child2) 
  {
    open STDIN "<&READ" or die "Cannot open read filehandle\n";
    exec ('grep', 'grep');
  }

waitpid ($child1, 0);
waitpid ($child2, 0);
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Of course being an unreformed Perl4 hacker I use file handles, there is no doubt a better way to do it.