All three of the above suggestions have merit.
1. You have a car that few mechanics care to work on because of its heritage and electronic uniqueness. I personally do not trust repair shops to do a quality job on anything. I do all my repair work here at the house any work with a Crossfire only amplifies that attitude. If you can't work on the car yourself plan on spending unnecessary money on repairs. THUS, as James said you need to know that new alternator that was installed is working properly, or did the shop give you a bad replacement. Perhaps a auto parts store can check the alternator for you and while there get the car scanned for trouble codes. If you ask nicely they generally will do the check and scan for free. You probably need a new battery. Get a copy of the owners manual if you do not have one! It is a free download on this forum
2. Your symptoms could be a number of things Relay Control Module (RCM) or perhaps the Crankshaft Position Sensor (CPS) or wheel speed sensor.
We have a member on the forum who repairs RCM for about $60.00 You email him first then send your RCM to him and he will return it quickly repaired and with improvements over the original. He wrote the thread I am about to link to click here Click for RCM info
3. If that doesn't fix your problem you probably need a CPS. YOU MUST PURCHASE ONLY THE BOSCH BRAND OF CPS.
use the search box on the top right of this forum and the google option to find more info.
Hope that helps and gets you started in the right direction.