This is just timing conflicts. The OP is trying to do something this software is not designed to do. It would be the same if he hooked up 2 CD players and had someone try to push play at the same time... only this is worse because there is no way to ask the system to even try to synchronize the music playback.
In this case, there are 2 separate devices with 2 separate CPU's. Yes, they may be linking into the same iTunes library on the same wired or wireless network. But pull those

TVs out of the equation and try to do the same with a couple of iDevices (also with independent CPUs). Without some software running to synch up the devices, they have no way of knowing when to start playback in unison with the other device.
It sounds like what the OP needs is for Apple to make multiple-Airplay functionality have some added code for synching. I doubt that's there now.
Instead of trying to do this with 2 largely independent systems, I suggest buying something made for this... something to take the output from a single

TV and push it to the 2 independent sets of speakers. Something like this:
http://www.iogear.com/product/GHPAKIT/
If the OP has a receiver, I'd run the audio out of the

TV into the receiver and then use the receiver to push the signals to more than one room. Someone mentioned a zone 2 receiver earlier. THAT (too) will work.