There are many, many possible issues here. But one of the most common is the use of improperly remanufactured alternators. I have seen three defective remanufactured alternators in a row for one vehicle come from a popular low priced parts store. This is such a common problem that I now absolutely refuse to buy a remanufactured alternator from any place except a NAPA parts store.
The second most likely issue is that the mechanic did not reprogram the replacement computer he installed on your vehicle (virtually all replacement computers for this vehicle must be flash reprogrammed when they are installed). If the first mechanic is willing to correct his mistakes and not charge you for the additional parts or work required to fix it properly; I'd give him a chance (but only at no additional charge). If he refuses to take responsibility for his actions; I would demand a refund for his incompetence; and would take legal action if he won't cooperate. Your local District Attorney or Consumer Protection agency is there to stop nonsense like this.
A mechanic who does not succeed in repairing a problem by replacing the parts he determined were faulty should not go on charging you for what were obviously wrong diagnoses, faulty replacement parts, or improper installation procedures. You are not subsidizing his schooling. If he tries to charge you for additional work; take the car to another shop that guarantees their work and have them fix it properly.