I'm typing this from my Mom's machine.

I had installed Avast! with an appropriate license, however it has been replaced by the 'trial' version of McAfee.

How do I prevent this from happening again?

Try using Revo Uninstaller to remove every last trace of McAffe.

http://www.revouninstaller.com/

Reboot, then install Avast or MSE or another free antivirus.

That is not the problem.

On all of the machines she has access to she's unwittingly uninstalled Avast for some McAffe [trial-ware] bundled with Adobe and/or [edit] Suite updates; is there a dummy instal that will block McAffe and prevent it from pulling this [BS]?