So... the dash lights go on with the key AND (I'm assuming) they go off when the engine is running AND you found negligable or no voltage drop on the positive side of the charging circuit AND you have the same symptom with a replacement alternator as with the first one.

You've got 3 possibilites; least likely is that you replaced a bad alternator with a defective rebuilt. Next least likely is that the ground wire is open because the dash lights went on (although it could have resistance causing a voltage drop under load). Most likely is one of those basic must-haves.

With the engine off, place your thumb on the alternator fan and push down firmly. Did it turn without a LOT of drag and without turning the crankshaft? You've just found the answer. I'll bet that the belt is worn too narrow and is slipping, regardless of how "tight" it seems by pressing on the belt itself. Vee belts get traction by wedging themselves into the groove and making tight contact on both sides of the pulley. If it rides down at the bottom of the groove, it cannot do its job. You have to put energy IN if you want to get energy OUT, spinning the shaft is not enough.