2005 Honda Odyssey Fan Relay

I have an extended warranty and I am actually putting it to use. (Hold the applause). I took my Odyssey in to the Honda dealership to get it repaired.
I noticed the problem while in a drive-through. I did not have any air on and I bent down to grab my purse and heard the sound of the air conditioner come on. It was cold so it surprised me I straitened and moved to turn air off and saw I was surrounded by a cloud of white smoke blowing through the vents and outside from my hood. I immediately pulled to the side and turned care off. Called my road-side assistance and was towed into the dealership.
They replaced a lot of air conditioner parts: compressor, w-condenser discharge hose, suction hose, condenser assembly, clutch set, stator set, a/c system - evacuate and recharge (what is this) and tested for leaks.
I got my car back by the end of the day. I was not taken out and shown what was done. I didn't know and I didn't know how A/C even worked. I know more today.
I drove home and parked in garage. Peace, I have my car back to chauffeur my 3 year-old, 20 month old and 1 month infant!
Next morning husband called his car died on way to work, may need the Odyssey. I go out and it is completely dead.-
I call roadside assistance. Someone comes out and charges my battery. It starts and we leave it running to help the charge. Roadside assistance leaves. I am trying to feed kids and make sure no one steals my running car outside. Suddenly, pop-pop-pop-pop, like popcorn popping as loud as gun shots. I race out and white smoke coming from my car. And the pop-ing sound is scaring me to death. I reach in and turn car off. DOUBLE CRAP!
I call roadside assistance and have car towed into another dealership because it is closer to my house than the other dealership. I find out at end of day the relay-switch has to be replaced.
Here's my question: my battery is dead, in order to get it off Honda lot it has to be running. They told me this, they know. I said it should be replaced because the part that was not replaced caused car to work harder and drained my battery. I am not asking morally should they change the battery. I am asking can the repairs from the first day cause my battery to discharge? Can not changing those parts cause my battery to discharge.