This may be an overkill, but why not use semaphores? In pseudo-code:

$SEM = CREATE SEMAPHORE;
IF ($PID == FORK())
{
    wait($SEM); # grab the semaphore
    open file;    
    WRITE 'ALPHA';
    close file;
    signal($SEM); # signal semaphore
    wait($SEM); # wait for signal from child
    open file;
    WRITE 'BETA';
    close file;
    signal($SEM); # signal semaphore
}
ELSE IF(DEFINED $PID)
{
    SLEEP(3); # make sure parent grabs semaphore
    wait($SEM); # wait for signal from parent
    open file;
    READ THE FILE;
    close file;
    signal($SEM); # done with file ops, signal semaphore
    wait($SEM); # wait for signal from parent that it is done writing 
+to file
    open file;
    READ THE FILE;
    close file;
    signal($SEM); 
}
[download]

In Perl, I would recommend using IPC::SysV. It seems better suited than just the Perl primitives. Here's a quick little Perl blurb (warning: untested).

use IPC::SysV qw(IPC_PRIVATE S_IRWXU IPC_CREAT);
use IPC::Semaphore;

my $sem = new IPC::Semaphore(IPC_PRIVATE, 1, S_IRWXU | IPC_CREAT);

$sem->setall( (0) x 10);

my $semid = $sem->getVal($sem);

if(my $pid = fork())
{
    $sem->op($semid, -1, IPC_NOWAIT);    #get the semaphore
    open(FILE, ">/myFile.txt") or die "error: $!\n";
    print FILE "Hello, my name is Perl.\n";
    close FILE;
    $sem->op($semid, 1, IPC_NOWAIT);    # signal semaphore
    $sem->op($semid, -1, IPC_NOWAIT);    #wait on semaphore
    open(FILE, ">/myFile.txt") or die "error: $!\n";
    print FILE "Hello, again, my child.\n";
    close FILE;
    $sem->op($semid, 1, IPC_NOWAIT);    # signal semaphore
}
elsif(defined $pid)
{
    sleep(3);
    $sem->op($semid, -1, IPC_NOWAIT);    #wait on semaphore
    open(FILE, "/myFile.txt") or die "error: $!\n";
    print while(<FILE>);
    close FILE;
    $sem->op($semid, 1, IPC_NOWAIT);    # signal semaphore
    $sem->op($semid, -1, IPC_NOWAIT);    #wait on semaphore
    open(FILE, "/myFile.txt") or die "error: $!\n";
    print while(<FILE>);
    close FILE;
    $sem->op($semid, 1, IPC_NOWAIT);
    exit(0); #exit child
}

$sem->remove;
[download]

Of course, that, again, might be an overkill. You could probably accomplish it with some extra file foo or so.

Jeremy