I think that you want to parse the string the same way that a shell parses a command-line. The result is a list of sub-strings. It probably is a good idea to do the validation (use previous suggestions) before attempting the parse. I cannot think of a good way to do the parsing. I hope I have put other monks on the right track.

UPDATE

You can parse the strings with Text::CSV

#!/usr/bin/perl
use warnings;
use strict;
use Text::CSV;

my @strings = (
    '"my" "dog"',
    '"my" "dog shepherd"',
    'my dog',
    'my "dog shepherd"',
    '"my "dog"',
    'my "dog shepherd',
);
my $csv = Text::CSV->new ( {sep_char => ' '} )
    or die "Cannot use CSV: ".Text::CSV->error_diag ();

foreach my $string (@strings){
    open my $fh, '<', \$string or die "Cannot open string";
    if (((my $temp = $string) =~ tr/"//) % 2){
        warn "invalid string";
        next;
    }
    my $row = $csv->getline($fh);
    if (!defined $row) {
        warn "getline failed";
        next;
    }
    close $fh;
    $" = ' | ';
    print "@$row\n";
}
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