Something I've done in the past (admittedly for cron jobs but could still be applied here) is have each script set a fail flag (a zero byte size file for example) that would tell the next script to exit without running.

In script2.pl:

if ($you_do_not_want_script3_to_run) {
   # create zero byte size file...
   open(FAILFLAG, ">/tmp/script2.failflag") || do {
      # handle the error here
   };
   close (FAILFLAG);
}
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Then in script3.pl:

my $script2_failflag = "/tmp/script2.failflag";
if (-e $script2_failflag) {
   # script3.pl should not contine any further
   exit();
}
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