The batteries showed that no charge was being applied
What is telling you the batteries are not charging? The chassis dash voltmeter and or the house battery meter?
Pulled the alternator out had it tested . It was in good working order
By whom? Was the alternator FULLY LOADED to the limit of its capacity (Example 120 amps for a 120 amp alternator)?
NUMBER ONE
Charge the batteries fully
Use a voltmeter. How many volts are present at the output stud of the alternator with the engine running.
NUMBER TWO
12.7 volts or less, alternator is BAD, based on the stator tap signal malfunction symptoms of your tachometer. You would get ZERO RPM reading with a bad alternator or bad voltage regulator control harness connections.
NUMBER THREE
Parts store alternator test machines are play toys, and the personnel operating them could not rebuild an alternator if their life depended on it. I've spent too much time with know-it-all parts store employees who in fact could not count past ten without unzipping their pants. Go to your yellow pages or search online for AUTO ELECTRIC REBUILDERS in your area. When they answer the telephone ask them if they rebuild their own alternators "on site". If they say yes, ask them how big the motor is powering their alternator test bench. If they do not know, or they say the motor is less than five horsepower, move on down the line.
What happens is this. A bad alternator can fool a parts store alternator "tester" so fast and so thoroughly that it makes a joke out of the whole operation. THE ALTERNATOR MUST BE TESTED TO FULL CAPACITY OF THE ALTERNATOR.
You want an example? A failed (open or shorted) in a Ford 3 or 4G.
The alternator will put out ENOUGH amperage to totally pull the wool over the eyes of a parts store alternator "tester". But the failed diode WILL NOT FOOL THE TACHOMETER especially if it has failed in the SHORTED manner.
I have to insert the following out of necessity rather than vanity. The OP may not be aware of my history.
Personally (with my own hands) rebuilt more than ten thousand automotive, diesel truck, commercial fishing vessel, bus, military and aviation (PMA certified) alternators.
Your description of the symptoms raised the hackles on the back of my neck. They do not add up to a parts store play toy machine declaring the alternator as being "good". If you had enough power to start the engine, you have enough power to operate a hall effect (not an alternator stator) powered tachometer. A mechanical drive tachometer would not care.
Many top notch "real" rebuilders produce a product far superior to a parts store "Look! It puts out electricity - box it up" L.A. rebuilt. Many parts store alternators do not charge well at low engine speeds, have daffy duck voltage regulators that have wildly different voltage setpoints than original equipment regulators.
An RV is HARD on alternators. You need the toughest most durable alternator you can lay your hands on. Or, change mounting hardware over to velco and wing nuts for easier monthly guaranteed-for-life replacement.