I'm wondering if this is because you're using the same DB handle to open the second connection before closing the previous one.

With use warnings;, you would have received a warning similar to:

"my" variable $dbh masks earlier declaration in same scope...
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Because you've declared it twice with my.

Try either disconnecting then reusing the same $dbh:

my $dbh = ...;
print "This works\n";
$dbh->disconnect;
...
$dbh = DBI->connect ... # no my declaration
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...or just using a different handle name:

my $dbh_1 = ...
...
my $dbh_2 = ...
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