Hi, J.. I'm guessing the wiping problem is after a bowel movement, yes? You should check your daughter's anal area to see if she has any irritation. A rash really hurts when it's wiped with plain toilet paper, and that may be what she's avoiding.
If so, get her some moist baby wipes with aloe vera, but no alcohol. You might not be able to see a rash, exactly, but she might have a sore bottom for some reason. Show her how to use the wipes, and see if she will use them herself. The aloe vera in the wipes will help heal any irritation she might have, and that should eventually solve the problem.
Do you have a new baby in the house, or has the family schedule changed in any other way so that your daughter gets less time and attention from you and other grownups? If so, she could be doing this for attention. She remembers when you used to wipe her, before she got to be such a big, grown-up, independent little girl. This may be a subtle way for her to ask you for more time, nurturing, etc. If she has gone through some kind of upset recently (or even not gone through anything -- she just might be feeling a sense of loss because she is aware she is growing and losing that baby-type nurturing), she might go back a few steps in her emotional growth and independence.
Try giving her a little more nurturing and attention in some other way, while gently reminding her that she needs to keep clean because that's what good girls do. You don't have to emphasize what BIG girls do because that might be what's setting her off -- she doesn't want to be such a big girl yet. But certainly she wants to be a good girl. Let her know how much she is loved in every other way, but don't put extra attention on the wiping thing. You can let her know how good the moist wipes feel, and how they make her skin soft. If she sees you using them, too, that's an extra incentive to use them herself.