When parsing strings I usually go for the 'brute-force' approach (I'm just that kinda guy), splitting around each char and testing one-at-a-time:

use feature ":5.10";
use strict;
use warnings;

my $line = "05/04/2010 13:09:45 - A - somebody - ( ( my.my id >= 1 ) )
+ and ( ( is-relative.to code = 'sister' ) or ( is-relative.to code = 
+'brother' ) or ( is-mother.to code = 'dog' ) )";
my $open = 0;
my @result = ('');

for my $char (split ('',$line)) {
    given ($char) {
        when ('(') {
            $open++
        }
        when (')') {
            $open--;
            push @result,''
        }
        default {
            $result[-1] .= $char if $open
        }
    }
}
[download]

That gives me:

  my.my id >= 1

  is-relative.to code = 'sister'
 or  is-relative.to code = 'brother'
 or  is-mother.to code = 'dog'
[download]

Which is not good enough, so I need some tidy-up:

for my $line (@result) {
    $line =~ s/^\s+(?:or\s+)?(.*)[ ><!=]=.*/$1\n/; 
}

@result = grep !/^\s+$/,@result;

print @result,"\n";
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Which gives:

my.my id
is-relative.to code
is-relative.to code
is-mother.to code
[download]

which I think is what you are looking for. Not sure that it is all that elegant though.