#!/usr/bin/perl -l
use strict;
use warnings;
use Text::Balanced qw(extract_delimited);

my $text = 'SELECT "SELECT * FROM table1 WHERE ..." SQL FROM table2 WHERE ...';

my (undef, $remainder) = extract_delimited($text, '"', '[^"]*');

my ($extracted) = $remainder =~ /(\bFROM\b.*?\bWHERE\b)/;

print $extracted;   # FROM table2 WHERE