No, you cannot include a Sonos Amp as part of your Arc/Sub/One SLs 5.1.2 setup. But you can add a second Sub to complete your 5.2.2 system.
Note, you can add a second Sonos Sub to the existing Arc setup.
You can ‘group’ the Arc Room with the Amp room, but for TV audio playback you will likely experience a 30-75ms audio lag, which will likely send any connected Amp speakers/3rd-Party Sub out of sync.
‘Grouping’ the devices (Arc & Amp) would be fine however for music audio playback as the audio is buffered on all products and will play in sync.
I’ve no experience with the ‘sound-shaker’ theatre seats, so can’t comment on that part of your post (sorry).
If the sound-shaker seats don’t produce any audio (don’t think they do), just vibration, then the delay may not be noticeable. It could out fairly well as you could turn the amp on/off (add and remove group) pretty easily.
The non-Sonos sub is a no go though. You are better off getting a 2nd sub if you want more bass.