Note that this would be a very un/anti-OO way to go about using OO methods. But here's a possibility:

my $obj1 = Package_one->new;
my $obj2 = Package_two->new;

my $results = $obj1->can('package_one_method')->($obj2, @more_args);
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The 'can' method will return a code reference to the first objects method, and then you can pass that method the second object, and more arguments if necessary.

You can probably expect to be 'deprecated' for using methods in this way, though. But hey, at least perl lets you do it, whereas other 'OO' languages wouldn't :-)

Update:Your second init method is using '$self' as if it were a hash, when it is a hash ref (it should be "$self->{'index_path'} = shift", not "$self{'index_path'} ..."). And the same thing goes for your first new method (should be "$self->{'access_log_path'} ...".