AV receivers that can do 3 zone multiroom are either going to be high-end, or you'll need something midrange with zone 3 out as a line level signal going out to a separate power amp. TBH though, it's a bit overkill for what you need unless you're open to buying a used amp.
The modern solution to this is amps such as Yamaha with a Musicast feature or Denon/Marantz amps with their version called Heos.
The basic idea is that the receiver does 5.1/7.1/Atmos for the cinema room, and then second and third and fourth and 5th etc zones are homes for either a wireless speaker or a zone amp then running a pair of conventional or in-ceiling speakers. This provides what you're looking for, which is any amp source spread across all zones but with individual volume control in each.
The Speakers A-B thing wasn't the same idea. It can be used for same source in two rooms, but the volume control works on both A and B in tandem rather than separately unless driven either A or B but not A+B.
Running A and B speakers at the same time isn't an issue unless the combined impedance rating is lower than 16 Ohms. Even then, as long as party-levels aren't needed it would be okay to pair 8 Ohm and 6 Ohm together; just watch the volume level.