I'm just use ing the CQLogin module in script A, so in this case I cannot use kill as there is no separate PID for script B, is that correct?

Suggestion 1:
Set interrupt to die, then use eval to trap the die in the code. This modification could be in either the primary module or the CQLogin module, depending on if you want to change the calling contract of the CQLogin.

Suggestion 2:
Use a parsing module that has already anticipated and fixed these issues.

#!/usr/bin/perl 

use strict;
use warnings;

my $INTERRUPT_MESSAGE = "caught sig int user interrupt";
$SIG{'INT'} = sub { die $INTERRUPT_MESSAGE };

my $login = new CQLogin();

my $username = eval { $login->autoLogon() };
if ( !defined $username && $@ ) {
    print STDERR "wow, we got a signal\n\n"; #just for demo purpose
    die $@ unless $@ eq $INTERRUPT_MESSAGE;
}
print "Success, our username is [$username]\n\n";

#note, username will be undef if the user interrupted.

package CQLogin;

sub new
{
    my $class = shift;
    return bless {}, $class;
}

sub autoLogon
{
    my $self = shift;
    chomp( my $username = <STDIN> );
    return $username;
}
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