NO DOUBT ABOUT IT...A&D OINTMENT (NOT THE CREAM). It's very thick and sticks on like Vaseline, but it works better than Vaseline because it's medicated. Lather it on after every diaper change and bowel movement.
It may hurt a little when you first put it on, but that's simply because ANYTHING you put on your daughter will make her feel sore when she's in that condition. The soreness goes away fast.
Regarding baths, baking soda may help because it has the salt effect, which heals skin.
Regarding some suggesting your daughter eat yogurt, this may work for some children, but pay attention to how it may effect your own child, because yogurt can give some children looser bowel movements (like my children). If your daughter will eat cheese, that may help slow down the bowel movements. String cheese is popular with kids. Like anything though, make sure not to give your child too much yogurt or cheese, because if it's not your child's norm, overdoing it can also have an adverse effect and upset her stomach (causing more bowel movements).
Make sure NOT to give your daughter anything acidic to drink, like fruit juices. Water is the best thing for them to drink. If you can't get her to drink water, sometimes simply adding ice cubes will attract children. If she refuses water, then Pedialyte is a good choice too. Also, keep her away from eating rich foods for the time being, which may upset her stomach (like red & white sauces or desserts). Keep food bland, like crackers or Cheerios for snacks.
I would be careful about letting your daughter run around without a diaper on. As long as their rash infected skin is covered and soothed by something like A&D Ointment, they should be fine and extra air won't be necessary. You don't want to take the chance of spreading dropped feces germs to yourself, to other children, or possibly even reinfecting your daughter at a later date. You may not know if you step in it or touch it since it will be on the floor or ground somewhere.
Good luck, and let us know what ends up working for your daughter!