Battery charge

The next time you start it with the remote starter, use an inexpensive digital voltmeter to measure the battery voltage while the engine is running. It must be between 13.75 and 14.75 volts. If it stays near 12.6 volts, the charging system is not being turned on.

If there's actually a problem with the generator, it should act up sooner or later while you're driving. General Motors has by far the worst design generator in the world. It is real common to go through four to six of them in the life of the vehicle, but they usually fail completely; they don't typically fail intermittently like on some other brands. You already did what many professionals are finding out will reduce the number of repeat failures. That is to replace the battery. In fact, since your battery was recently replaced, that might save your generator from failure. Because of their design, these generators develop huge voltage spikes that interfere with computer sensor signals, and they can destroy the diodes and internal voltage regular inside the generator. As they age, batteries lose their ability to dampen and absorb those voltage spikes. The old battery will often work fine in a 1986 or older model vehicle.

Being not familiar with remote starter systems, to me that would imply there is an intermittent problem in the generator. That is not common. 13.0 volts is too low but suggests the system is at least partially working since it's higher than the voltage of a fully-charged battery. 14.8 is getting a little high but nothing to worry about if it doesn't go any higher.