The kids situation is one I cannot address directly, other than saying to keep it out of their view as much as possible.

As for the testing, it is a natural thing, and one that I tend to encourage. This allows her to feel free to speak up when there really is a problem. Talk to her, and if it really bothers you l let her know, and then point it out when she does it.

My advice would be to let her test you, as in the long run it will give her more faith in you, and you in yourself.