A two port controller would be ideal. But if you need to use what you have, lets walk through this.
As far as audio, you have only one input to the controller. You can try to parallel both receivers audio to the one input. They should be high impedance and line level. They should mix OK. If there is a volume level issue between the two you'll have to pad down the higher volume to even things out then maybe adjust the drive to the transmitter if need be. The down side is if a WX alert is going off and somebody keys up the repeater and talks, it will just be a mish-mash. You are also open to more hum or noise depending on ground loops, etc.
For the COR I see a problem with the WX receiver. It has an alarm output, but looks like you can select only eight seconds or five minutes for the output duration. Too short or way too long in my opinion. What I would do is set it for eight seconds and have it trip an external timer. The timer output would in turn pull the COR input to the controller to ground. Set the timer to about a minute should give enough time to relay the voice announcement without tripping the time out timer. I use a lot of these, they're cheap...