You're not comfortable, and the provider wants you to part ways. Then it's a done deal.
I'm not sure how you overpaid, unless your child's father is paying some of it and you aren't aware of those payments. But if she went off on a tangent, she's not focused enough to provide care or she's deflecting your attention from other irregularities. She said you owed money, but in fact she owes you money? She's either unethical or she's disorganized. Either way, red flags.
Is this "friend of a friend" licensed to provide child care? If not, get out anyway (regardless of your feelings) and find a neutral provider where there are more standards.
From your other post, it seems that your son's father isn't particularly sensitive to your feelings. I hope you find enough backbone to do what you think is best for your child and stop being pushed around or influenced by what others think you should do.