So I guess that the reason you try cloning the database handle is to reuse the connection parameters?

In that case, you can just write a sub that returns a closure which in turn creates a database handle with all the right parameters.

sub get_dbh_factory {
    my @config = @_;
    return sub {
        return DBI->connect(@config);
    }
}

sub somewhere_else {

    my $dbh_factory = get_dbh_factory( ... );

    if(fork == 0) {
        my $dbh = $dbh_factory->();
        ...
    } else {
        my $dbh = $dbh_factory->();
        ...
    }
}
[download]

Code above is sloppy and just a sketch, but the principle behind should work.