EWR likes to funnel people through P4 because it reduces the traffic in front of the terminals. Your case reveals how this policy can seem a bit wacky, but overall the system works fairly well (as long as the Airtrain isn't broken).
If you are doing this at an odd hour, you may be able to convince the shuttle driver to take you directly to P4, but dont count on it. You will have no luck getting a hotel shuttle to pick you up at P2 or at Alamo. The extra stop at P2 may add 5-10 minutes to your trek, so don't worry too much about it. If your hotel shuttle isn't one that runs continuously, call the hotel from P2 to get the shuttle rolling and reduce your wait time at P4.