Try using Meguiars number 2. Its called "Fine cut cleaner". Its meant to be used with a rotary or orbital buffer/polisher. I used it on my car and it will remove almost any stubborn scratch or swirl mark. Be sure to use a foam bonnet w/ it. Avoid terry and wool bonnets. They have a cleaning action and with a cleaner/abrasive like this, they'll only add more swirls. If the scratches and swirls are too deep for this to get it out, then Meguiars has one more prodcut you can try called "heavy cut cleaner". Its number 1 I believe in their line up. Its a 7 on the scale of aggressiveness but it might work if the fine cut cleaner fails. You can follow up either of these formulas w/ Meguiars number 9 fine swirl mark remover and then some number 7 polish to make it luster. Then, just coat it with some wax and you should be set.
EDIT: Here is my overall recommendation.
Orbital buffer/polisher w/ foam bonnet
Meguiars number 2 - fine cut cleaner(if the swirls are so deep this can't remove it, then try number 1 - Heavy cut cleaner)
Meguiars number 9 - fine swirl mark and scratch remover(this will remove any small swirls the number 2 leaves behind)
Meguiars number 7 - show car gloss(its a pure polish that will make the car luster)
Meguiars number 26 - Hi tech yellow wax. This is just a pure wax that will protect the work you've done
It's a bit of work, but the results will be great.