def check all your wiring.

unfortunately there are quite a few things that can cause these problems and pinpointing them could be a matter of trying a load of different things to test components.
FIRST OFF -- After you changed your alternator, did you change your battery? If not, your battery was dead and thats the reason it won't hold a charge any more even after you bought the new alternator.

If its a new battery, try these checks --
First do what kirk said, check that your battery is securely strapped/bolted/ fastened down in some manner.
Check the tightness of each of your pos/neg cables to the battery posts.
Check to see that the cable isnt cut into weird anywhere or for some reason any bare wiring isn't showing/rubbing against another metal thing (such as a brake line/cable)
Check the grounding spot for the negative cable, clean off any sitting oil/coolant/water/grime, this will probably not do much other than help it out a little.
Try running a new grounding cable. This is easily done using a 4-2 gauge wire commonly found for about 5 or so bucks at walmart. Make sure to find a spot on the chassis where it seems to really be solidly built and drill a hole through it, sand off all of the paint until you get bare metal, put the cable through there and seal it in with a nice thick bolt, to make sure it doesn't rust in the future, put some sort of anti-corrosive agent on it.
run a new ground from your alternator (it will be very small, like 12-14 gauge) Put a beefy 8-4 gauge on it and do the same thing as where you grounded the battery's negative cable

If none of these work, LMK - PM me