electric problems
 

i have a 96 dodge 2500 and i know the heating elements in the intake to heat the air takes alot of juice but it pulls the alternator which is new down to charging 12.40 then when its cycle stops it charges back to 14 but when i turn the fan full blast with the lights on the oil pressure gauge goes up and the volt meter drops down. I had both batterys check and they tested good ones 2 years old and the other one came in the truck when i got it. Also when its cold the engine doesnt turn over as fast as it should but it fires up but when it does it takes the alternator a bit to charge up to 14 like as soon as i fire it up volt meter reads 12 then like 1 min later it goes up to 14. idk if a new battery to replace the one that was in the truck will fix the problem? the battery in the truck doesnt say what brand or how many craking amps when i got it tested we just used the other battery to compare and it held 13 volts should i replace it?