my $stdout_and_stderr1;
my $stdout_and_stderr2;
my $stdout_and_stderr3;

{
   print "running script1.pl\n";

   local *STDOUT;
   close(STDOUT);
   open(STDOUT, '>', \$stdout_and_stderr1) or die("...");

   local *STDERR;
   close(STDERR);
   open(STDERR, '>&STDOUT') or die("...");

   do 'script1.pl';
}

{
   print "running script2.pl\n";

   ...