First, don't rub her head in it. That does nothing other than make her want to hide from you when she does it so instead of starting to use her litterbox, she'll go behind the couch or under the bed or somewhere that you can't get her. That is, obviously, NOT what you want her to do.
How often are you cleaning her litterbox? Some cats will not go in their litterbox unless it is spotless so if you aren't cleaning it everyday, you may want to try that.
What are you using to clean the spots where she goes? Make sure you use a good enzyme killing cleaner. Nature's Miracle and Simple Solution are good ones.
Is there a pattern to where she goes? For example, one of my cats will urinate on loose pieces of fabric. If you leave the bath mat down, she'll pee on it. If you drop laundry on the way to the washer, she'll pee on it. If a pillow case falls off the shelf, she'll pee on it. There's nothing wrong with her, I had the vet check her out. I avoid it by making sure the bath mat is picked up, I don't drop any pieces of clothing, and all the pillow cases/sheets/towels are put away so that they don't fall. If she's going in a certain spot, you may need to make sure you are using a good cleaner or try moving a piece of furniture over the spot so she can't get to it.
The vet is a good place to start though. No sense in punishing her for something she can't control if it is an infection. Plus, the earlier things like that are caught, the easier they are to treat (not to mention slightly less expensive).
Also, is she spayed? If not, getting that done may help. We were dumb with our first cat, thinking she's an indoor cat and the only cat so why waste money getting her spayed. When she was around 6 or 7 she started occassionally peeing outside of her litterbox. Someone finally told us that getting her spayed might help that so when she was about 8 we got her spayed and she never had another incident outside of her box.
If the vet says there's nothing wrong with her, try a calming collar. A lot of people I work with use them on their cats and swear by them.
As far as the washing, you can use just plain, original Dawn dish soap. Don't get the fancy scents or anything with bleach. Make sure it is the ORIGINAL Dawn.