Not charging with headlights on

I would clean the battery terminals, and not just the posts, but also where the cables enter the clamps. Then clean the terminal at the starter relay where the power take off point is to go into the car. Then the engine ground. Then the ground strap from the engine to the body.And finally from the radiator core-support back to the battery. Then I would check the battery fluid level,and put the battery on an automatic trickle charger for 2 or 3 days. Then I would clean the regulator case and it's mating surface.
Then I would do a full-field test on the alternator.
If you still got problems, then we will really have to get into it.

Of course it could just be a shorted bulb.You would have to unplug them one atta time, and leave them out. If all the bulbs are out, and no difference, then we will really have to get into it,lol