I can confirm the above behaviour with the latest version of Avast. Actually, the Avast on the remote connection is not completely frozen. If you send a CTRL-ALT-DEL request, it triggers the standard Windows blue screen, from which selecting the Task Manager takes focus from the Avast window and the remote connection can be used again.
I was trying to exclude the DWservice daemon from being scanned by adding all sorts of exclusions to the Avast installation to no avail. It would be really useful to have the exclusions working on Avast, I have the same negative experience also with executed script programmes on Windows (Perl and Pyton), where regardless of any formulated exclusions, Avast is still checking them fully (as can be seen from the processor load during their execution).