battery getting drained while driving

Well, the 14.7 V reading says that the alternator is basically working OK, although that is a bit high. The drop to 12.6 V at lower idle is presumably due to the fan load at the lower RPM's.

I was going to ask about the belt; serpentines have been known to slip without a really tight tension, moreso than V's. Twice, I have had a similar problem with a V belts looking right and having tension but getting polished on the belts' contact surface and did not run the alternator at speed (each time, it was one of those stupid Top Cog types) and ran down the battery both times on a long interstate speed drives with a lot lower current draw. The battery ended up with a similar low voltage as your reading. When the belts get at speed, they can arc out in funny ways that they don't at idle speeds and fool you and slip, plus I assume they will stretch a bit when hot.

Is the smooth side of the belt on the alternator pulley or the grooved side? Howm much torque do you have to put on the tensioner pulley to make it move? If it is not a lot, then you probably do not have enough tension.

Next drive, rig the voltmeter onto the system and put it in the seat beside you and monitor the voltage directly.