Using two bluetooth profiles at the same time to make a wireless keyboard
One possible solution is to treat of the two wireless part-keyboards as separate independent keyboards i.e. Bluetooth HID keyboard devices.


Each of the parts has only a subset of keystrokes it can send to the host.
The two parts do not need to know about or interact with each other (if there is such a need, this solution is no longer a contender).
That way, if a particular application needs only numeric, or only alphanumeric inputs, that keyboard alone could be used independently.
The host Bluetooth device (tablet, PC, ...) needs to pair with both HID devices.