Groovy
Sharing with you my personal experience.
My ex ex ex ex helper main duty was to look after my girl. She was good with her duties but as she was quite experienced, she tend to like to do things her way. We close one eye as she seems to be very good with my girl.
When my daughter was about 2, this maid left her alone to play in the living room and went into the kitchen to prepare for dinner, (though we told her not to do other things when my girl is not sleeping) and my girl climbed up to the dining table and swallowed her father's cough tablets and I rushed her to Kk. They had to resuscitate her as her heart almost stopped from all those pills she swallowed. Thank god she survived.
I feel that since you no longer trust your maid, then no point keeing her. Trust is very important since you're entrusting Josie in her care. You'll be worrying about her every minute, how to concentrate on your work? No doubt she's good with Josie, but If she can ignore your instructions now, who knows what else she can do next time? And if her main duty is to look after Josie, then it's better for her not to do housework when Josie is awake. If you still feel uneasy or she still ignore your instructions, then change before another incident happen. The salt, the lying down, those lies, what's next?
Nowadays very hard to get good helper. The last helper i had, we treated her so nicely, yet she climb over our head. So now, I'd rather save the trouble of getting myself angry and just do without a maid. More work, but less headache!