The battery isn't getting a charge while driving and you got a new altenater new battery and you checked the grounds Its got you stumped?
Did you have the new alternator tested before you installed it?
I have already purchased aftermarket parts from places like
Autozone and installed them and have found they are defective. I
installed a starter only to find out the starter was bad. I took it
back to Autozone, they gave me another one, I asked to have it
tested and IT was defective. I had to go to another store to get
one that worked. freak of nature? Maybe ...but it does and has
happened. Make sure the belt on the alternator isn't slipping.