Ask your shop to do the basic charging system/battery test. A diy’er could do something similar: Before first start of the day the battery should measure about 12.6 volts. Immediately after starting the engine, 13.5-15.5 volts. What do you get?
Also be aware on modern cars that whenever the battery is disconnected (which was probably done to replace the alternator) the engine computer may lose its learned parameters, and that can cause rough idle, hard to start, etc when the battery is re-connected. Usually that problem will resolve itself after a few drive cycles. But sometimes the car has to be kick-started back at the dealership with an idle-learn procedure.