No I dont understand that either. If connecting just the 12V GND wire (without the +12 connection) is making a difference then either your grounds are not already common, or something else (eg rfI ) is affecting it.
How do you know "the motion sensor works fine" when there is no output ? the HC12 is adding complexity; i'd suggest you put an LED on D12 to show the PIR state.
You aren't thinking R2 on your schematic is the "pull down" are you?