In my version (Socket6 is 0.22 and Socket is 1.82) when I try your code I get:
"AF_INET6" is not exported by the Socket6 module

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Inspecting the code somewhat I see in Socket6.pm:
push @EXPORT, qw(AF_INET6) unless defined eval {Socket::AF_INET6()};

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and indeed the version of Socket.pm I have does export AF_INET6. Changing your code a little works for me:
use warnings;
use strict;

use Socket qw(AF_INET6 AF_INET inet_aton inet_ntoa);
use Socket6 qw(inet_pton inet_ntop);

BEGIN {
  require Exporter;
  require DynaLoader;
  our @ISA = qw(Exporter DynaLoader);
  our @EXPORT = qw(AF_INET AF_INET6);
}

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Maybe you need some sort of test in a BEGIN block to see if the user's Socket.pm exports AF_INET6.

In reply to Re: Trying to cleanly re-export another Module's export constants by cdarke
in thread Trying to cleanly re-export another Module's export constants by pprindeville

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