Issues after changing alternator

4-5 month's ago I took our car into a mechanic who said my alternator
needed to be changed. (didn't have much power). after changing it, battery
started oozing. Mechanic say's to get another battery. Which I did and has
been working fine.

Car was fine until the alternator. Since then, When I first start the car in the
morning (or after it's sit for about 6-7 hours) it start's up - airbag & battery
light STAYS ON until the car goes into a revving mode. Revving mode I'm
referring to is that the car while parked will start idling higher, as if I'm
holding pedal which I'm not btw completely on it's own. It'll rev up & down
for about a minute and while it's doing this the lights in the car including the
dash will flicker off & on. After it goes through this mode then it's fine,
airbag/battery light goes off.

If i turn on the AC at all which has been getting worse as well, it'll make the
car run rough. Sometimes if i don't hit the pedal she'll die out while driving
when AC is on. (HAVE to run AC our son had a transplant & can't breathe
the construction air around here)

Took her to a different mechanic yesterday who charged us $640.00 and
said ONE issue i would have to take to dealership. A computer, in the
dashboard thing. Then what he fixed was (a coil in the starter??) as well as
changed the spark plugs and said the whole light flickering etc shouldn't
happen.

Well, it's still doing the same today. And I'd like your opinion's before I try
another mechanic. mahalo.