he best way to do this, IMO, would be to use a proper DSP, like a Biamp Tesira Forte...
Tesira Forte unit only. NOT INCLUDED. wire connectors. power cord.
www.ebay.com
It will provide you enough inputs for all of your sources and allow you to implement duckers for mixing the audio as you choose. The output can be setup as you choose as well.
What you want is such a niche case, that no specific audio product does what you want exactly. You could use a hardware ducker and a mixer in front of it for the outputs of the 3 different radios, but at the end, it won't offer any serious customizing which it sounds like you may want to do.
Unfortunately, it's not like the Biamp unit is super straightforward to program and it is a 120v unit, not a 12v unit and would take a good minute or two to boot up every time you turn the vehicle on.
There are no car solutions I have heard of for this specifically. If I wanted to keep it really low profile, I might get a RDL mixer for the mics, and a RDL ducker, if they make one, as they are super small and easy to hide and power up quick enough.