If this doesn't work than yo may have to get an estimate at a body shop to wet sand your vehicle.
I use Meguire's, only from experience. I tried other stuff I had laying around and they simply did not work as well as Meguire's.
1. Prep Paint. Wash vehicle w/ dish soap to rid it of grease and wax build up.
2. Use Meguire's Clay Bar w/ lubricant to rid the paint surface of contanements. You may
have to use some elbow grease on the hard stains, like the one you have pictured. If
this does not work then you may have to get an estimate from the body shop for a
wet sand, because using the clay bar is the last attempt before wet sanding.
3. Wash again w/ car wash soap, this is get rid of the Clay Bar residue.
4. Use Meguire's Scratch X, this will also help w/ removing surface junk and fill in the
minor scratches. BE ADVISED use this stuff in tiny sections, because it's hard to get
off if left on too long.
Your paint should look 100% better by now and it should feel like glass. The Clay Bar will make it feel as smooth as a baby's butt, like it should be. If you run you hand over the paint right now, it may feel "gritty" and the Clay Bar will fix that.
You can stop now if you'd like, but to make it even more shiny, do the rest.
5. Use Meguier's Polish. If you think your paint looks and feels good now, try this stuff.
The polish will give it that wet look.
6. Seal in your hard work with the Wax. I use the Meguire's liquid wax.
I would take before and after pictures just to see the difference. Also PLEASE DO THIS IN THE SHADE!! My Aunt waxed her car in direct sunlight and the wax was burnt into the paint, you do not want that happening.
If it's cloudiness thats bugging her this stuff will help 110%. So good luck, and if you hate it use dish soap to take it all off.