Your alternator is charging just fine. It sounds like your battery may have a dead cell or two.
You may get the battery bench tested at a battery center. I have purchased "new" batteries before that were ultimately found to be defective months and even weeks later. Then return your battery for a replacement or a full refund (hope you saved your receipt).
2009 ML350 (84K) - Family vehicle
2001 CLK430 Cabriolet (71K) - Wife's car
2005 BMW 645CI (124K) - My daily driver
2012 Mustang V6 (60K) - Daughter's car