I'd create a role for creating children, and let each class consume the role while parameterizing its child's context:

#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };

{   package Child::Creator;
    use MooseX::Role::Parameterized;

    parameter context => (isa => 'Str', required => 1);
    role {
        my ($p) = @_;
        my $context = $p->context;

        has _child_context => (is => 'ro', default => $context);

        sub create_child {
            'Child'->new(context => shift->_child_context);
        }
    };
}

{   package Parent;
    use Moose;
    with 'Child::Creator' => {context => 'parent'};

    __PACKAGE__->meta->make_immutable;
}

{   package Teacher;
    use Moose;
    with 'Child::Creator' => {context => 'teacher'};

    __PACKAGE__->meta->make_immutable;
}

{   package Child;
    use Moose;
    use Moose::Util::TypeConstraints qw{ enum };

    has context => (is       => 'ro',
                    required => 1,
                    isa      => enum([qw[ parent teacher ]]));

    __PACKAGE__->meta->make_immutable;
}

my $p = 'Parent'->new;
my $ch_p = $p->create_child;
say $ch_p->context;

my $t = 'Teacher'->new;
my $ch_t = $t->create_child;
say $ch_t->context;

# Attribute (context) is required at constructor Child::new (defined a
+t ./1.pl line 44) line 30
my $ch = 'Child'->new;

# Attribute (context) does not pass the type constraint because: Valid
+ation failed for '__ANON__' with value "unknown" at constructor Child
+::new (defined at ./1.pl line 44) line 39
my $ch = 'Child'->new(context => 'unknown');
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But you haven't described what you need the context for, there might be better ways to get there.

Update:

The parameterized role is not needed here, it just keeps the context closer to the role consumption. You can use a plain Moose role, too (but there are cases where you can't replace a parameterized role with a plain one):

{   package Child::Creator;
    use Moose::Role;
    requires 'child_context';

    sub create_child {
        'Child'->new(context => shift->child_context);
    }
}

{   package Parent;
    use Moose;
    with 'Child::Creator';
    sub child_context { 'parent' };

    __PACKAGE__->meta->make_immutable;
}

...
[download]

($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,
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