Ok. After annoyingly hard work, I've got the following code that works! Now, obviously, it works on the data structure you've given and returns the output you desired. I make no anythings when it comes to any other data structures.

my @tables_seen;

sub traverse_nodes {
    my ($db, $start, $record) = @_;

    push @tables_seen, $start;
    my @records = ("$record");

    CHILD:
    foreach my child (keys %{$db->{$start}{$record}{children}}) {
        next CHILD if grep /$child/, @tables_seen;

        my @child_values;
        foreach my $key (keys %{$db->{$start}{$record}{children}{$chil
+d}}) {
            push @child_values, traverse_nodes($db, $child, $key);
        }

        my @temp = @records;
        @records = ();
        foreach my $rec (@temp) {
            push @records, map { "$rec $_" } @child_values;
        }
    }

    return @records;
}

my $starter = 'table a';
my @good_records;
foreach my $record (keys %{$rdb->{$starter}}) {
    @tables_seen = ();
    push @good_records, map { join "", $_ }
         traverse_nodes($rdb, $starter, $record);
}
print "REC: $_\n" foreach @good_records;
[download]

------
/me is the brightest bulb in the chandelier!