Battery not staying charged, new bat. And ALT.

Although your problem is most likely a short somewhere (very hard to find. Or give advice on), it may be possible that you suffer from the same problem that I had years ago on my old Pontiac Lemans. I was driving home one night with no indication on the dash that anything was wrong. When I stopped for gas, I had to boost the car to restart. I got home, tightened the alternator belt and had no further problems. The alternator must have been turning but not enough to run the car and charge the battery and there was no squealing sound from th belt slipping to warn me.
I recommend you check the tension on your serpentine belt. You may have a weak tension pulley.

I've had the same problem, on my car and replaced both items also, It turned out to be a bad connection with the battery termanals, they build up a corrosion film, you need to take off the connectors and use a wire brush or sandpaper on the battery connectors themselves.
When they are coroded it will have green/blackish film on them.
Try that, I would be surprised if that did not work.