Hi,
If you're getting 14,5V at the alternator and 13,5 at the battery, you have a big voltage drop across the main charging circuit. I had something similar and ignored it for so long it set my alternator on fire. The main feed from the alternator runs from the 8mm bolt on the back and down to the positive terminal on the starter. From there, the charge runs back to the battery through the heavy gauge starter cable. To diagnose, start by CAREFULLY clipping a good jumper cable from the alternator output bolt to the battery positive terminal. Do you now get roughly the same voltage across the battery as you get at the alternator? If not, add a second jumper from the engine block to the battery negative terminal. If your alternator and battery are anywhere near OK, you should now have the same voltage at the battery and alternator. Depending on which jumper had the desired effect, you now know where there's a weak connection. Find it and fix it. On mine, it turned out to be the cable between alternator and starter. It's routed quite intricately and re-terminating it under the car was a pain, so I simply unbolted it from the alternator, cut off the cable shoe and insulated the end well. I then fitted a new heavy-gauge cable directly from the alternator output to the battery. No trouble since.
Good luck!