Sorry to argue the point with Optima battery folks, but most cars and trucks have at least a 100 amp alternator that is regulated to put out 14.6 volts when charging. I have used alternators many times to recharge a dead battery when lights or some other load has fully discharged the battery. You may damage the alternator if the battery is bad but I have never had a problem in 45 years of auto ownership and using the alternator multiple times to recharge a dead battery. They usually charge up in less than 30 miles of driving to full charge and enough to crank the car again in as little as 10 minutes if the battery is good and only accidently discharged. Not long back I had completely drained my truck battery by leaving my trailer (with electric brakes) hooked up, it wouldn't even run the radio or even a dash light, jumped it off and ran it 25 miles with charge at 14 volts according to the gauge. Stopped loaded up my tractor on the trailer, cranked up and headed home, about 10 miles down the road the ammeter went back to about 13 volts indicating battery was fully charged. Still using that same battery. This is at least 2 times this battery has fully discharged and several times it has set for 8 months at a time and discharged with the security system on to be so low it barely started. No alternator troubles.
Tractors have smaller alternators generally speaking than cars so it would take longer to charge, but I cant see it damaging the alternator as long as the voltage regulator is properly working, it wont overload the capacity of the alternator. It may be better on the battery to do a slow 6 amp charge like most battery chargers do, but so far it hasn't hurt the 2006 year made battery in my 2007 truck.
I would agree with you that alternators CAN and do recharge what seem to be dead batteries. However in the OP's case she clearly had the two deadest batteries in the known universe.
It seemed to me from what she said that the first battery had been replaced because it was no longer taking jump starts, and in Nov.'012 they replaced it with another fresh battery, which lasted admirably until just recently.
You give examples of draining batteries to a no charge state and then jumping them to then use the onboard alternator/regulator to bring them back to life. This can and does work, EXCEPT the OP's case is different. From the time of insertion of the second battery the dead short in the glow plug relay never allowed the new battery to regain a full charge. It, the drained battery AND the shorted glow plug relay, were constantly drawing so many amps out of the alternator that it could not provide the necessary output for a long enough time to bring the battery back to a fully charged state. Basically it could not overcome the combined load of the relay's draw and the battery's marginal state of minimum charge. With your vehicles you would find the battery dead and correct the drain, headlights, trailerbrake, whatever, and then have a NO LOAD condition for the alternator to correct, except for recharging the jumped battery. This was not a constant drawdown of your battery to a state of near complete discharge.
I do disagree with Optima's statements about alternator damage occurring, as if it always is a problem when trying to recapture a marginal or deeply discharged battery.
More later- 'gotta run out....
I'm back now - additional factors play into the entire scheme of battery failures or 'potentially' dead conditions. One is specific gravity- a measure of the electrolytic level of each cell in a conventional wet cell battery. Without each cell having enough water and acid a battery can end up with one or more sulfated cells, rendering it unable to handle the loads placed on it by the car, truck, tractor, boat, etc.'s electrical system. Water in the electrolyte mix of wet cell batteries can and will evaporate over time, especially in high heat conditions in various parts of the country. If caught in time distilled water can be added to bring the level up to the split ring level in each cell.
Another factor is a properly run load test, to determine the exact state of the battery's ability to handle a load of a certain # of amps for a specific time frame.
Without these tests being properly executed it's anybody's GUESS as to what a battery can or can't do under load in a vehicle of any type.
Years ago when I had my foreign auto shop I owned a Snap-On load tester and it worked great in determining if a battery was marginal or in need of replacement.