Note that wait returns -1 if there are no more children, so this caught my eye as being a little unsafe:

...
  my $pid = wait;
  if ($pid == $pid1) {
    ...
    $pid1 = -1; # indicate child1 has been reaped
  }
...
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If somehow you get out of sync with wait and it returns -1, you might interpret it incorrectly.

I would code the reaping loop something like this:

while (1) {
  my $pid = wait;
  last if $pid < 0;
  if ($pid == $pid1) { ... }
  elsif ($pid == $pid2) { ... }
}
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For a non-blocking version of wait, see perldoc -f waitpid.