I kinda knew this might happen...

My car has been having a hard time starting- even when its not bone cold out.. And when I drive, it jerks and loses power -or diminished power anyway- in this rhythmic pulse. I thought maybe it was the fuel pump. But today I left the lights on (old car) and the battery was of course dead. So I called AAA for a jump. Almost an hour and a half later the truck shows up. (We had to sit in the car and the wind chill is -5 and the regular temp is 17 or something! But at least we were out of the wind.) He tested the battery various ways and eventually declared that it was a bad battery because his little electronic sensor thingie told him so, which he showed me. So he offered me a new battery. I- good or bad- said yes. Only because my car has been driving with that pulsing and almost not starting every time I go to start it! And its been going on even when it was warm out! So, that was that. I paid for the battery and the car sprang to life! Driving it felt GOOD! It had so much power! Now, I'm worried it might be my alternator that is killing my battery?? But that's just a wild stab in the dark. At any rate, once we left the parking lot of Home Depot (where it died) it was all zippy and happy and ALIVE! I felt good. But of course, i called my mom and told her and her husband got all up in arms saying the old battery had been under warranty and it hadn't been that long since we'd gotten it (I have no idea when we actually got it) and he wanted to get the old one back and get my money back, etc. I hate that my mom puts everyone on speaker phone with her Iphone so her husband hears everything I say! I didn't call him on purpose because I thought he'd freak out- and he did! So we left it as is. I guess I'm the idiot that's out a bunch of money. Meh. I hope the car stays zippy! But now I feel bad because of what my mom's husband said and did. (He called the place he says we got the old battery and talked to them.)