Perhaps you should look into IO::Tee since you are trying to write to two different filehandles at once.

The following is to be considered psuedocode since I don't have your full source code:

use IO::Tee;
my $tee = IO::Tee->new("|$externalprogram",">>$log");
print $tee <<EOJ;

(lines to send to external program)

EOJ
[download]

Note: you may have to use it in conjunction with IO::File.