Electrical problems, bad alternator - need opinion

Hey. Over a long period of time if anybody remembers i've been trying to pin point the problem to my vibration and dimming lights and so on.

I did the BIG 3 (grounding) but that did not help. I came to a conclusion that it is my electrical system and most likely the alternator.

Now, what i did is test the battery using my volt meter. With Car off it reads a bit over 12V, but bellow 13V. With car running it is 13.7-14 V. Now when i put a load on my car, such as braking or turning A/C or heater, the voltage drops and goes back up to the same mark. That's when the dimming of the head lights, dome lights, odometer display happens.

Is this normal ? I don't think so. Should the alternator keep up the consistent voltage when a load is introduced ?
I would also like to mention that the voltage drops slightly, not a whole lot. It doesn't not go below 12V when a load is introduced.

Any ideas ?