Can a Antivrius be used for two machines by mapping the hard drive of ther other

Using the solution with mapped drives dramatically reduces the security on several aspects.

First, and just as u mentioned, it cant scan the memory or the running processes. And it cant scan the startup config or the registry, which is very important.

Secondly, by using the mapping protocols (I assume ur using Windows), poses a Huge security risk all by itself.
You should never use file sharing or anything like that in Microsoft, because if 1 of the computers get infected by a virus (probably the 1 with no active AV protection), it might infect the other computer aswell.
It you need to use file sharing, I suggest u use a standalone network drive that connects to the router, with no system behind it to execute any code (like on a computer).

The drawbacks with mapped drives and 1 antivirus (to mention a few): It uses alot of ur bandwidth (LAN) and that might even affect ur routers performance (due to router of course). It use alot of time consuming CPU and can be a mess while scanning the other computer when its not in idle. U might even have priviledge access problems with the mapped drive.

Recommendation: Just as the people above me said, its Not recommended to use this method in a home network environment. Its only good for an enterprise network with a centralized antivirus database. I agree AVG is a good antivirus, but I would recommend Avast (also free) which is 1 step better to my experience.