Mrs Carr's name was Katherine. Katy, as her first daughter, would be named after her and also given the nickname Katy to better differentiate between the two. Supported by Phil being named after Dr Carr and going by Phil rather than Phillip.
Mrs Carr died giving birth to Phil
Mrs Carr died giving birth to Phil as she passed away around the time that he was born and Death by Childbirth was a sadly common trope in those times. However there are also brief allusions that Mrs Carr was, or at least had become, a sickly person at some point in her life which may have played a large role in her eventual death.
Katy can't have children
Katy still doesn't have children come the end of In The High Valley despite being Happily Married. Her famous fall from the swing as a child, or the treatment following it, may have left her infertile. Especially as she's a Friend to All Children and would most likely love to have her own while Ned is away at sea.
Alternatively, Katy having to raise her younger siblings meant that she simply didn't want children right away once she got married, as it gave her the much-needed freedom she never had as a child.
Mrs Florence and Mrs Nipson knew that the note wasn't from Katy or Clover
There are so many reasons that couldn't have been from either of the Carr girls;
"Dear Berry, - I saw you last night on the green. I think you are splendid. All the nuns think so. I look at you very often out of my window. If I let down a string, would you tie a cake to it, like that kind which you threw to Mary Andrews last term? Tie two cakes, please; one for me and one for my room-mate. The string will be at the end of the Row. "Miss Carr."
Examples of both Katy and Clover's letters show that they have a much more sophisticated style of writing, and both teachers would have access to their schoolwork to be able to draw comparisons.
Neither Katy nor Clover was even at Hillsover 'last term'; how could they possibly know about what kind of cake Mary Andrews had or that it had been thrown to her in the first place? Additionally, how would they even know who 'Berry' is?
Finally, Katy and Clover are known for being intimate with one another, and surely they would have used the term 'sister' rather than 'room-mate'.
So why do Mrs Florence and Mrs Nipson continue to insist otherwise? They're still sore about the fact Katy's refusal to use a communal washroom led to all of the students ordering private washstands for their rooms and wanted to punish the sisters for it, without making it obvious. It was just a happy coincidence that the note gave them a good reason to place them in a less pleasant room.
Susan Coolidge originally only intended on writing What Katy Did and What Katy Did At School
As evidenced by the following paragraph from What Katy Did At School;
And with that morrow, when she (Katy) came out of her pretty room and took her place once more as manager of the household, her grown-up life may be said to have begun. So it is time that I should cease to write about her. Grown-up lives may be very interesting, but they have no rightful place in a child's book. If little girls will forget to be little, and take it upon them to become young ladies, they must bear the consequences, one of which is, that we can follow their fortunes no longer.
Followed by the Bookends of her opening What Katy Did and ending What Katy Did At School by listening to the katydids in a field.
