Well, from my understanding of the docs (of which I quoted parts in my previous post), this ought to extract the inner ZIP file from the outer ZIP file, into a string: 
use IO::Uncompress::Unzip qw(unzip $UnzipError);
my $file = '2.zip';
my $inner;
unzip $file, \$inner, Name => '1.zip';

[download]
after which you can continue: 
my $txt;
unzip \$inner, \$txt, Name => '1.txt';

[download]
and now the text will be in the string $txt. (Caveat: untested)

Apparently the "Name => $name" part is optional if the ZIP archive contains only one file (what they call a "member file"):

Say you have a zip file, file1.zip, that only contains a single member, you can read it and write the uncompressed data to the file file1.txt like this. 
unzip $input => $output
        or die "unzip failed: $UnzipError\n";

[download]

If you have a zip file that contains multiple members and want to read a specific member from the file, say "data1", use the Name option 

unzip $input => $output, Name => "data1"
        or die "unzip failed: $UnzipError\n";

[download]

In reply to Re^3: Reading a .txt file under 2 levels of compression by bart
in thread Reading a .txt file under 2 levels of compression by LazyIntern

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