I'm not sure how much you paid, but you basically got two very different systems and they shouldn't cross over (or at least not much).
The 3700 is great for a surround sound area. If you have proper surround sound you need to setup, then the 3700? Perfect!
The AMS and the 12 channel amplifier are all about stereo audio distribution. They can be bridged, but generally don't need to be, and not something I would do. But, can support up to 6 rooms (12 channels) of stereo audio in a space. The AMS itself, can send audio from up to 8 sources to up to 8 rooms total, but you still only have amplification for 6 rooms of stereo.
Here is the type of way that this type of equipment is used together...
So here we go... 24+ A/V Zones w/10 Sources | Audioholics Home Theater Forums
Yes, a controller unit is generally needed for the AMS of some sort. I haven't messed with one before, as I use Crestron's similar version, the BIPAD8 which is a 16x8 audio matrix. The important thing is the remote selection of audio sources to any zone, along with volume control. Super cool feature to have in a home or a larger business with multiple areas in it which may need it.
Heck, I set it up in a client's home where they could push a microphone to multiple areas of their choosing with the touch of a button. Then touch the button again and it would revert to playing whatever audio was going on. (He holds parties at his home from time to time)
So, I assume the 8x8 is also a pre-amp along with audio selector. The amp can drive the speakers across multiple zones accurately.
The 3700 is for a primary surround sound zone, like a theater space.
Nothing wrong with the rack or the subwoofer to have in the mix as well if it works for your setup.