Since a lot of people are reading this post here is a summary of the solution:
Invite each of your alts to your party and go into Broadcast mode (PgUp by default) and enter the command /gcp lockparty.
This will do two things:
Keep your GCP addon from using extra resources in Battelgrounds and Dungeons which will likely cause the interface to crash.
And if your party gets split up in battelgrounds by the system the addon will make it as if though you are still in the same party. You can still monitor each members health, mana, and casting and all of your commands will continue to function. Very very useful.



I tried typing in all the orders again right before joining. It fixed all the bars disappearing, but when battlegrounds started my toons were split up into different groups, and my framerate still dropped to 1 frame per second, even though my computer is not under any stress, CPU usage looks perfectly normal around 50%. Only my main WOW window is running at 1 frame per second, the others are running well over 30 frames per second.
It also seems that if anyone in my party disconnects, it drops my fps of my main window back to 1. This is not a performance issue, there is something strange going on with the party system.
Also why do I need to re-type the order every time I am about to go into battlegrounds?