Engine squealing when first started up.

Ok, so this is my wife's car and when she goes to leave in the morning for work/school her 2005 Kia Rio will start squealing really high pitched. After she drives it a little bit (like out of our apartment complex onto the main road, not even a mile) it will stop. However, if she turns the a/c or just the fan by itself on it will start the squealing again. If she drives and gets the engine completely warmed up (driving for like 20-30 minutes) she can turn the a/c and fan on and it won't squeal. If she stops driving, turns the car off and leaves it off for a few hours while she is at work or whatever and comes back to get in and come home it will do all this all over again. Any ideas on what this may be? Her dad has some experience with car repairs (he is not a mechanic) but he said it may be the alternator not giving enough power? Also, a side problem that may have something to do with this is that it idles really hard. At a stop light the engine will be running at like 700RPM and the whole car is shaking including the steering wheel which shakes violently. If we raise/lower the power windows it lowers the rpm's of the car and makes it vibrate/shake even more. Thanks for your help!