=for discussion
The Problem:
    The problem is labelled in My::Main::Child1->usechild().
    We wish to access the LWP::UserAgent object, located
    in the blessed hashref of My::Main::Child1's parent
    (My::Main is the parent in this case).
=cut

# My/Main.pm
package My::Main;

use strict;
use LWP::UserAgent;
use My::Main::Child1;

sub new {
    my ($class) = @_;

    my $self = bless( {}, $class );
    $self->{_ua} = LWP::UserAgent->new();

    return( $self );
}

sub newchild {
    my ($self) = @_;

    return( My::Main::Child1->new() );
}


# My/Main/Child1.pm
package My::Main::Child1;

use strict;

sub new {
    my ($class) = @_;

    return( bless( {}, $class ) );
}

sub usechild {
    my ($self) = @_;

    # PROBLEM LINE!
    my $res = $self->(...)->{_ua}->get(
        'http://www.example.com'
    );

    return( $res->code(), $res->content() );
}


# usemain.pl
#!/usr/bin/perl -w

use strict;
use My::Main;

my $main = My::Main->new();
my $child = $main->newchild();

my ($code, $content) = $child->usechild();