I used to detail cars, and this is a common problem I had to deal with. The low cost detail shops use a quick/heavy cutting polish or compound then covered up the swirls with a glaze that hides the scratches tempoarily.
You'll need an orbital buffer and fine polish to remove those. It will be a ton of work, but you may also be able do it by hand depending on how severe they are. The best I found was Griot's Garage who offers a random orbital buffer, foam pads, and polish/wax kits. I had alot customers come to me after doing the same thing your daughter did- use a cheap place that left swirls- and two weeks later they'd have their car at my place to fix (using Griot's products) what the "bargain" shop messed up.
Here's their website:
http://www.griotsgarage.com/
And the kit I'd reccomend. It's $199.00 but worth every penny. You said that money was tight, but this is cheaper than paying a good detail shop to fix your paint. You could try doing it by hand first but it that doesn't work you'll need a buffer, and these are the best at a good price.
http://www.griotsgarage.com/product/...ortby=ourPicks
Here's one of their videos on youtube showing their orbital buffer.
http://www.youtube.com/watch?v=2m7Lp...ature=youtu.be