Alternator and engine failure nightmare?

I was driving and my radio began to cut out, then shut off completely. After another 4 blocks my lights all shut off and then another 2 blocks my engine shut off completely. I was unable to get it to start again and determined it was a bad alternator. I replaced the alternator and then within 24 hours (approximately 100 miles driven) plastic casings around that alternator melted and my vehicles engine shut off while I was diving a second time and left me stranded for 5 hours. I was told the alternator must have been defective and put a second alternator in. Everything seemed fine for a week and then suddenly, it wouldn't start when I came out of the store. I was able to get someone to use jumper cables and it was fine for another week. This time as I am driving, my ABS light will come on and then my radio will cut off, then the transmission light comes on, then the head lights and dash lights shut off, then the engine. I have had the battery tested and when it is fully charged, I was able to drive the 25 mins (18 miles) home but around mile 20, the ABS light had come on and the dash lights shut off. Please help.