Alternator replacement?

My car was making some weird noises upon starting and fuses were going out rapidly along with a headlight I had just replaced going out, so I brought it in a repair shop and told them to diagnose the issues and get back to me. They came back with the engine mounts needing replacement for $750.00 so, I got that fixed and left in my car. Less than a week later and only driving the car maybe 2-3 times since leaving their shop my car won't start at all and I have to have it towed back to the same place. This time they came back with needing to replace both the battery and the alternator for $1,200! My question is, how in the world did they not catch this the first time I went in with the car?