"What if live view was disabled while recording, or conversely, if recording stopped when live view is accessed?"
Ah, good point! I see where the complication comes in. If live view was disabled while recording, then recieving a motion notification earlier may be pointless, as we can't be sure if it's actually an intruder, an animal, a false alarm, etc. In addition, it could potentially put people in a dangerous situation if it actually is an intruder or a dangerous animal, and they decide to go outside or to wherever the camera is to check it out.
The second idea I like more. The down side to having recording stopped when live view is accessed, is people would probably want the intruder recorded on camera. I mean, you could always snap shot the screen from your smart phone, but having a recording is much better. However, maybe if a warning came up that stated the recording would stop if trying to access the live view? Even though people may like to have the camera recording in this kind of situation, at least we have the notification early, and the option to view it if we want.
So, with the input of you guys, my suggestion is:
Notification of motion as soon as it is detected. When trying to access live view, have a warning stating the recording will stop.