My sister had her car painted by Maaco. We cleaned that car as well as possible before taking it there. Well, while it was out, a bird crapped on it. They didn't clean it, and they painted over it. Her car was a 94 Plymouth Sundance, and it's paint was peeling too. The Maaco job kept it looking decent for about six months, and then it started to flake off too.
The best way to handle this problem on your car is the cheapest way but the most labor intensive. Since you own a white car, it is super easy to match because there is no metallic flek in the paint. So, you go to your auto parts store, and by a couple different grades of sandpaper, some grey primer, and paint. MAKE SURE YOU LOOK UP YOUR CAR IN THE PAINT COLOR MATCH GUIDE! Since you have a white car, I'm 95% sure that you'll find a match right on their shelves.
Sand all of the loose paint off of the car. If the paint and primer have peeled and it is rusting, then sand out the rust. (Use a coarser grit paper.) Remove the dust with a tack cloth or paper towel. Just make sure you remove it all. Prime it with two coats of primer, then paint it with at least two coats of paint. Make sure to let it dry between coats. Do this in the sun on a hot day with low humidity if possible. Paint with even strokes and a constant distance from the car. Make sure not to apply too much paint at one time. (Make sure you mask off all of the areas that you don't want paint/primer on!)
This will take you about a day to do correctly, and it will look fine on a white car. (Make sure that you mix the paint completely by shaking for about five minutes before spraying on the car.) If you don't like the way it looks, then you are only out about $20, and can have someone else paint it. I had a lot of luck with this method on my white Plymouth Reliant. Just take your time and be careful with the paint, and it should turn out fine.