You got 13.9 v charging from alternator? Not too bad, just a touch low. However, 13.4v from your charger? NOT GOOD at all. You are never getting the battery full at that voltage. First, you NEED to spend the money to get a good 3-4 stage charger, such as a PD or other, that will charge in the mid 14 v range. Until you do that, you will NEVER get good battery performance. You will be amazed how much longer your battery charge lasts.
When charging at 13.4 for a couple hours, you are lucky if you are getting to 60% or so full. So, does not take much to take battery down. Since you take your battery down until lights dim, and things quit, you are taking the battery down to near 0%. You should only discharge to 50%.
You are killing the battery! The dealer is correct. Get a good charger, and save your batteries.
