I ran ssh with -v and the problem is that it is sending only a bit of the command: 
system("ssh -qv $ssh_user\@$bkp_destination 'sed -i \"s#.*$hostname#$s
+key#g\" /tmp/test.txt'");

Variables:
$hostname = "HOSTA";
$skey = "ssh-rsa AAAAB3NzaC1yc2 root@HOSTA";

SSH output:
...
debug1: Sending env LANG = en_GB.UTF-8
#ssh-rsa AAAAB3NzaC1yc2 root@HOSTA#g" /tmp/test.txt
...

[download]
So it is not sending the entire -- sed -i \"s#.*$hostname -- bit.

In reply to Re^3: Send password in Net::SSH::Expect by gafaman
in thread Send password in Net::SSH::Expect by gafaman

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