Best method to remove buffer marks

[RexDodge]

Hi Guys. So this is my daughters Acura TSX. She bought some discount coupon for a "hand wash and wax". I cautioned her about having anyone wax her black car. She confirmed with the shop owner that it would be a hand wax and not a buffer job. Well as you see by the picture...it was buffed by a goon with little or no expeirience. I saw this when she brought it home and pointed it out being very sensitive to not say I told you, yadda, yadda. She called the owner and he said they would make it right. Took it back in and when she picked it up they walked the car (in sunlight) and she thought it looked good. When she got home it sat in the driveway for about a week. Then she drove it on a rainy day. I got home that afternoon from being gone about a week so I have not seen the car since the detail shop worked on it for the second time. I thought it had not even been touched from the first time! Swirl/buffer marks all over the darn thing! I show this to my daughter and she is livid. It's like whatever they put on the car to make it look better washed off while driving it in the rain. I did some research on the shop and the owner. This guy and the shop are a piece...of work. Many complaints and I find out the business license (and most likely insurance and bond) are expired. I took the car to a trusted body shop that has done work for me and they say the marks should come out. I then go to the shop and they offer to do it again. No way am I having them touch the car. They won't budge and won't pay for the repairs. I will end up doing this myself. I have buffed many cars but only a few black vehicles as I know my limits. I am in the middle of preparation for said daughters wedding and that means cash is non existent so taking the care to be buffed is not happening. Can you guys (whom I trust more that anyone) give me some tips on getting these marks out? It really looks like they are in the clear. Thanks