Question: What does she even do? The kids are too old for a nanny.
Question: This might be a stupid question, but why do all three of the children speak in typical American voices? Wouldn't their speech have a British influence because of their father, and also Niles?
Answer: Children's brains and language skills are still developing at that age and they adapt to the environment they live in. My former boss was born in England and moved to the US at about eight years old. She completely lost her British accent by her teens, even though her parents still spoke as typical English citizens. A Japanese co-worker and his wife, also Japanese, spoke English as their second language. Their two children learned both English and Japanese simultaneously while growing up and spoke each language with the appropriate accent.
Answer: Kids tend to take on the accident of where they live. I once had a British student who lost his accent after a couple of years in the US.
Not just where they live, but also after their peers (who live there, but you know what I mean).
Answer: Not necessarily. Their late mother being American would've probably made the most impact on their speech, considering most kids spend most of their early years more with their mothers than fathers.
Gracie is young enough that she doesn't remember her mother. The episode "I Don't Remember Mama" was about this.
Answer: Mr. Sheffield needed someone to manage the kids, not necessarily babysit them. Brighton was a Bart Simpson type, Maggie was shy and awkward and Gracie had personality issues.