False Accusations

Have you ever been falsely accused by the ex or the kids? If so, what happened and how did you handle it?
In my case, I was not actually accused of doing something improper, but the implication was undeniable. The ex made it known that she would rather have my step-son be at her house, by himself, than to have him spend even a couple of hours with me if my husband and/or step-daughter were not going to be at our house. I was angry and deeply hurt!
I have always treated both kids the way I believe I would treat my own. Is it wrong for a mother to be alone in a house with her son? Of course not.
But it's different because he isn't my son.
One of the most frustrating aspects of this part time step parenting is the double standards. I mean, it's ok for me to do certain "motherly" tasks such as cooking their meals, washing their dirty dishes, and chauffeuring them to practices and appointments, but that's about it. My opinions about how to help the kids with their problems are not only disregarded, they are completely unappreciated even though I sincerely care about the kids' well-being. But I digress.
Up until now, the only incident that has come close to a false accusation was when the kids developed a rash...several days after leaving our house. The ex wanted to know if I had washed their clothes, maybe in a new detergent. I suppose that was a reasonable question, but at the time, I was tempted to take it as an insult because I was hurt. Again, I try to do things that improve the health of my "family"--like buying detergent free of perfumes, dyes, etc--so even the suggestion that something I might have done (in an effort to help lighten the ex's laundry load) could have caused their rashes was upsetting to me.
Maybe I'm overly sensitive, but it is difficult enough to avoid getting roped into the image of the Wicked Step-Mother without unwarranted expectations of foul play.
I hope this incident doesn't mark the beginning of a new pattern.
So far, I have not made a big issue of her comments and her apparent belief that her son is not safe in my care unless a chaperone is present. But how would you feel? What would you do?
My theory is that trying to "clear my name" would only create more drama. I have done nothing wrong, so I have no need to defend myself.
But by making her position known, she has potentially made things a little more complicated for herself.
Just a few days before the unspoken accusation, she asked me to take her son to a practice. This required me to be with him in the van-without the supervision of his sister. But now that I know she truly doesn't trust me, I am no longer qualified to perform this service for her. In the future, she will have to make other arrangements or he won't be able to go.
Any thoughts?