As for switching between screens, currently you do need to drop the connection and reconnect to move to another monitor.
As to the mouse issue, it sounds more like an OS driver stack issue. What OS are you using on the Management system and AMT client?
A few more questions
Can you take a moment and compare behaviors between RealVNC plus and RealVNC plus. Let me know if there is a behavior difference in regards to the mouse control.
What OEM and model is the AMT Client?
Download RealVnc Plus