M.G.
ETA:
I think the car seat thing isn't necessarily related to language - that sounds like she's not up to date on what's safe. We had the same problem with my MIL and other relatives. We just provided all car seats/high chairs/gear - period. Lesson learned - problem solved.
As for language - If you say 'you cannot handle an emergency situation for us' - it might make little sense to her, because you hired her when she would have had less english.
That's the part I'm not fully understanding.
Plenty of people leave their children with relatives with little english, who may be even be older (e.g. grandmothers) and feel perfectly safe. Not to be judgmental - but maybe you're just anxious because of her recent accident. Keep in mind, emergency situations are pretty rare and typically they have someone who can handle different languages.
I do think it was unrealistic to expect her to learn a new language in 5 months.
My brother hired nannies who were not english speaking from another country to care for his children, and to live with them. They had enough basic english to get by. He hired them through an organization. They met the requirements.
He could make his concerns known (if any) back to the organization. I don't know if he had any, but I don't think safety was ever one of them. I don't know if you went through one or not.
If you have to let her go, I think you just have to be honest and say you thought you'd be ok with the language barrier but realize, you're always feeling somewhat anxious. You feel this isn't a great fit and you are sorry - you hadn't thought things through fully. Own it. She really hasn't done anything wrong. You say she's sweet and the kids adore her.
I'd give her PLENTY of notice, and great recommendation and work with her while you look for someone you feel more comfortable with.
Good luck