rough idling stalls and now is bucking-check engine light on

Sounds like you have a bad misfire. I would not drive the any longer as you risk serious damage to the engine every mile you drive. Here is a link so you can find a different repair shop in your area. Its always good to get a 2nd opinion and having 3 alternators put on in 3 months is not acceptable. https://repairpal.com/repair-shops Alex

There are several possible reasons this is happening .. A scan test is the best first step for diagnosing the issue .. You can go to a parts store for a simple code read OR better yet an auto repair facility that can do a complete scan test which is a lot more informative. Hands-on testing must be done to find the culprit .. In reality - just posting a list of the possibilities is not much help to you in resolving this problem.