If you have 13+ volts on the coach batteries while on shore or with engine running. Then all is fine with both of those charging systems, at face value. When you take these away and the batteries drop to 10 - 11v, you have one of two problems.
1. The batteries were very low and you have not charged them long enough (assuming you may have just got it out of storage) In that case you want to charge for 12-24 hrs and make sure batteries are topped off with distilled water.
2. Your batteries are shot and will no longer hold a charge. Have them load tested at a shop you would purchase new batteries.
John & Clare Lyon
2007 43.5' Monaco Dynasty Palace III (All Electric)
Towd: 2011 Chevy Equinox