Your use of escaped brackets in the second regex leaves me uncertain about your original data... because my first thought was that you misunderstood the use of a character class. But on second thoughts, and taking a wild guess what at what the data might be (a number inside square brackets, in the original string), this example may clarify:

#!/usr/bin/perl
use 5.016;
use strict;
use warnings;

# 1039350

$_ = "  this is a number [12345]   ";

if(/^\s*(.+)\s*/){
    say "in outter 'if', \$1: $1";
    $_ = $1;
    if($1 =~ /\[(\d+)\]/){
           say "\t But in inner if, \$1 : $1";
       }
 }

=head output:

in outter 'if', $1: this is a number [12345]
         But in inner if, $1 : 12345

=cut
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A couple points, beyond those made above:

• In your title, "Perl $" is not particularly good shorthand for "Perl vars" as the $ sigil specifies only one of several kinds of variables
• Including a data sample is usually useful, and often clears up ambiguities
• perldoc perlre and company will be helpful.