copying to shard drive while shared drive is streaming causes disconnection.

Hi,

I have an iMac, MacBook Pro Retina (both Mountain Lion), 2 Apple TV's and various iOS devices (latest iOS) all tied together with the Airport Express. The iMac is set up to share files and is essentially a home server. It has 2 external HDD's connected to it (2TB & 1TB). The 2TB is media storage and the 1TB is for the Time Machine. I have Plex Media Server set up on the iMac and can stream to any device I like. From my MacBook I can of course read/write to the 2TB and backup to the 1TB. It usually works perfectly. However, recently I've tried copying (a relatively large file, 10gb) from the MacBook to the iMac 2TB ex-hard drive while simultaneously streaming media (using airplay mirroring) from the iMac (again on the 2TB external hard drive) to an Apple TV and while Time Machine on the MacBook is backing up around 30gb of data to the 1TB external hard drive on the iMac. The copy and back up wont complete because the MacBook and iMac lose their connection with each other. At this point the picture being streamed to the Apple TV freezes (only on the ATV, it's still playing on the iMac) and the iMac will no longer mirror to the ATV without a restart of both devices.

Am I asking too much of my devices to be trying to do all of this at once? Or is there something I can do to resolve this so the devices don't lose their connections with each other and so the streaming and mirroring from iMac to ATV is not disrupted? Any help would be appreciated.